Solve 830/760*10^5*0.456=(0.24/16+0.29/M)*8.3*3*10

$$\frac { 830 } { 760 } \times 10 ^ { 5 } \times 0.456 = ( \frac { 0.24 } { 16 } + \frac { 0.29 } { M } ) \times 8.3 \times 3 \times 10$$

Solve for M

$$M=\frac{58}{39997}\approx 0.001450109$$

Steps Using Factoring

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1520M, the least common multiple of 760,16,M.

$$2M\times 830\times 10^{5}\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 2 and 830 to get 1660.

$$1660M\times 10^{5}\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Calculate 10 to the power of 5 and get 100000.

$$1660M\times 100000\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 1660 and 100000 to get 166000000.

$$166000000M\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 166000000 and 0.456 to get 75696000.

$$75696000M=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Expand \frac{0.24}{16} by multiplying both numerator and the denominator by 100.

$$75696000M=\left(\frac{24}{1600}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Reduce the fraction \frac{24}{1600} to lowest terms by extracting and canceling out 8.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 8.3 and 3 to get 24.9.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 24.9\times 10\times 1520M$$

Multiply 24.9 and 10 to get 249.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 249\times 1520M$$

Multiply 249 and 1520 to get 378480.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 378480M$$

Use the distributive property to multiply \frac{3}{200}+\frac{0.29}{M} by 378480.

$$75696000M=\left(\frac{3}{200}\times 378480+378480\times \frac{0.29}{M}\right)M$$

Express \frac{3}{200}\times 378480 as a single fraction.

$$75696000M=\left(\frac{3\times 378480}{200}+378480\times \frac{0.29}{M}\right)M$$

Multiply 3 and 378480 to get 1135440.

$$75696000M=\left(\frac{1135440}{200}+378480\times \frac{0.29}{M}\right)M$$

Reduce the fraction \frac{1135440}{200} to lowest terms by extracting and canceling out 40.

$$75696000M=\left(\frac{28386}{5}+378480\times \frac{0.29}{M}\right)M$$

Use the distributive property to multiply \frac{28386}{5}+378480\times \frac{0.29}{M} by M.

$$75696000M=\frac{28386}{5}M+378480\times \frac{0.29}{M}M$$

Subtract \frac{28386}{5}M from both sides.

$$75696000M-\frac{28386}{5}M=378480\times \frac{0.29}{M}M$$

Combine 75696000M and -\frac{28386}{5}M to get \frac{378451614}{5}M.

$$\frac{378451614}{5}M=378480\times \frac{0.29}{M}M$$

Subtract 378480\times \frac{0.29}{M}M from both sides.

$$\frac{378451614}{5}M-378480\times \frac{0.29}{M}M=0$$

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5M, the least common multiple of 5,M.

$$\frac{378451614}{5}M\times 5M-378480\times 5\times 0.29M=0$$

Reorder the terms.

$$5\times \frac{378451614}{5}MM-0.29\times 5\times 378480M=0$$

Multiply M and M to get M^{2}.

$$5\times \frac{378451614}{5}M^{2}-0.29\times 5\times 378480M=0$$

Cancel out 5 and 5.

$$378451614M^{2}-0.29\times 5\times 378480M=0$$

Multiply -0.29 and 5 to get -1.45.

$$378451614M^{2}-1.45\times 378480M=0$$

Multiply -1.45 and 378480 to get -548796.

$$378451614M^{2}-548796M=0$$

Factor out M.

$$M\left(378451614M-548796\right)=0$$

To find equation solutions, solve M=0 and 378451614M-548796=0.

$$M=0 M=\frac{58}{39997}$$

Variable M cannot be equal to 0.

$$M=\frac{58}{39997}$$

Steps Using the Quadratic Formula

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1520M, the least common multiple of 760,16,M.

$$2M\times 830\times 10^{5}\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 2 and 830 to get 1660.

$$1660M\times 10^{5}\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Calculate 10 to the power of 5 and get 100000.

$$1660M\times 100000\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 1660 and 100000 to get 166000000.

$$166000000M\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 166000000 and 0.456 to get 75696000.

$$75696000M=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Expand \frac{0.24}{16} by multiplying both numerator and the denominator by 100.

$$75696000M=\left(\frac{24}{1600}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Reduce the fraction \frac{24}{1600} to lowest terms by extracting and canceling out 8.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 8.3 and 3 to get 24.9.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 24.9\times 10\times 1520M$$

Multiply 24.9 and 10 to get 249.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 249\times 1520M$$

Multiply 249 and 1520 to get 378480.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 378480M$$

Use the distributive property to multiply \frac{3}{200}+\frac{0.29}{M} by 378480.

$$75696000M=\left(\frac{3}{200}\times 378480+378480\times \frac{0.29}{M}\right)M$$

Express \frac{3}{200}\times 378480 as a single fraction.

$$75696000M=\left(\frac{3\times 378480}{200}+378480\times \frac{0.29}{M}\right)M$$

Multiply 3 and 378480 to get 1135440.

$$75696000M=\left(\frac{1135440}{200}+378480\times \frac{0.29}{M}\right)M$$

Reduce the fraction \frac{1135440}{200} to lowest terms by extracting and canceling out 40.

$$75696000M=\left(\frac{28386}{5}+378480\times \frac{0.29}{M}\right)M$$

Use the distributive property to multiply \frac{28386}{5}+378480\times \frac{0.29}{M} by M.

$$75696000M=\frac{28386}{5}M+378480\times \frac{0.29}{M}M$$

Subtract \frac{28386}{5}M from both sides.

$$75696000M-\frac{28386}{5}M=378480\times \frac{0.29}{M}M$$

Combine 75696000M and -\frac{28386}{5}M to get \frac{378451614}{5}M.

$$\frac{378451614}{5}M=378480\times \frac{0.29}{M}M$$

Subtract 378480\times \frac{0.29}{M}M from both sides.

$$\frac{378451614}{5}M-378480\times \frac{0.29}{M}M=0$$

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5M, the least common multiple of 5,M.

$$\frac{378451614}{5}M\times 5M-378480\times 5\times 0.29M=0$$

Reorder the terms.

$$5\times \frac{378451614}{5}MM-0.29\times 5\times 378480M=0$$

Multiply M and M to get M^{2}.

$$5\times \frac{378451614}{5}M^{2}-0.29\times 5\times 378480M=0$$

Cancel out 5 and 5.

$$378451614M^{2}-0.29\times 5\times 378480M=0$$

Multiply -0.29 and 5 to get -1.45.

$$378451614M^{2}-1.45\times 378480M=0$$

Multiply -1.45 and 378480 to get -548796.

$$378451614M^{2}-548796M=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 378451614 for a, -548796 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$M=\frac{-\left(-548796\right)±\sqrt{\left(-548796\right)^{2}}}{2\times 378451614}$$

Take the square root of \left(-548796\right)^{2}.

$$M=\frac{-\left(-548796\right)±548796}{2\times 378451614}$$

The opposite of -548796 is 548796.

$$M=\frac{548796±548796}{2\times 378451614}$$

Multiply 2 times 378451614.

$$M=\frac{548796±548796}{756903228}$$

Now solve the equation M=\frac{548796±548796}{756903228} when ± is plus. Add 548796 to 548796.

$$M=\frac{1097592}{756903228}$$

Reduce the fraction \frac{1097592}{756903228} to lowest terms by extracting and canceling out 18924.

$$M=\frac{58}{39997}$$

Now solve the equation M=\frac{548796±548796}{756903228} when ± is minus. Subtract 548796 from 548796.

$$M=\frac{0}{756903228}$$

Divide 0 by 756903228.

$$M=0$$

The equation is now solved.

$$M=\frac{58}{39997} M=0$$

Variable M cannot be equal to 0.

$$M=\frac{58}{39997}$$

Steps for Completing the Square

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1520M, the least common multiple of 760,16,M.

$$2M\times 830\times 10^{5}\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 2 and 830 to get 1660.

$$1660M\times 10^{5}\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Calculate 10 to the power of 5 and get 100000.

$$1660M\times 100000\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 1660 and 100000 to get 166000000.

$$166000000M\times 0.456=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 166000000 and 0.456 to get 75696000.

$$75696000M=\left(\frac{0.24}{16}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Expand \frac{0.24}{16} by multiplying both numerator and the denominator by 100.

$$75696000M=\left(\frac{24}{1600}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Reduce the fraction \frac{24}{1600} to lowest terms by extracting and canceling out 8.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 8.3\times 3\times 10\times 1520M$$

Multiply 8.3 and 3 to get 24.9.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 24.9\times 10\times 1520M$$

Multiply 24.9 and 10 to get 249.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 249\times 1520M$$

Multiply 249 and 1520 to get 378480.

$$75696000M=\left(\frac{3}{200}+\frac{0.29}{M}\right)\times 378480M$$

Use the distributive property to multiply \frac{3}{200}+\frac{0.29}{M} by 378480.

$$75696000M=\left(\frac{3}{200}\times 378480+378480\times \frac{0.29}{M}\right)M$$

Express \frac{3}{200}\times 378480 as a single fraction.

$$75696000M=\left(\frac{3\times 378480}{200}+378480\times \frac{0.29}{M}\right)M$$

Multiply 3 and 378480 to get 1135440.

$$75696000M=\left(\frac{1135440}{200}+378480\times \frac{0.29}{M}\right)M$$

Reduce the fraction \frac{1135440}{200} to lowest terms by extracting and canceling out 40.

$$75696000M=\left(\frac{28386}{5}+378480\times \frac{0.29}{M}\right)M$$

Use the distributive property to multiply \frac{28386}{5}+378480\times \frac{0.29}{M} by M.

$$75696000M=\frac{28386}{5}M+378480\times \frac{0.29}{M}M$$

Subtract \frac{28386}{5}M from both sides.

$$75696000M-\frac{28386}{5}M=378480\times \frac{0.29}{M}M$$

Combine 75696000M and -\frac{28386}{5}M to get \frac{378451614}{5}M.

$$\frac{378451614}{5}M=378480\times \frac{0.29}{M}M$$

Subtract 378480\times \frac{0.29}{M}M from both sides.

$$\frac{378451614}{5}M-378480\times \frac{0.29}{M}M=0$$

Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5M, the least common multiple of 5,M.

$$\frac{378451614}{5}M\times 5M-378480\times 5\times 0.29M=0$$

Reorder the terms.

$$5\times \frac{378451614}{5}MM-0.29\times 5\times 378480M=0$$

Multiply M and M to get M^{2}.

$$5\times \frac{378451614}{5}M^{2}-0.29\times 5\times 378480M=0$$

Cancel out 5 and 5.

$$378451614M^{2}-0.29\times 5\times 378480M=0$$

Multiply -0.29 and 5 to get -1.45.

$$378451614M^{2}-1.45\times 378480M=0$$

Multiply -1.45 and 378480 to get -548796.

$$378451614M^{2}-548796M=0$$

Divide both sides by 378451614.

$$\frac{378451614M^{2}-548796M}{378451614}=\frac{0}{378451614}$$

Dividing by 378451614 undoes the multiplication by 378451614.

$$M^{2}+\left(-\frac{548796}{378451614}\right)M=\frac{0}{378451614}$$

Reduce the fraction \frac{-548796}{378451614} to lowest terms by extracting and canceling out 9462.

$$M^{2}-\frac{58}{39997}M=\frac{0}{378451614}$$

Divide 0 by 378451614.

$$M^{2}-\frac{58}{39997}M=0$$

Divide -\frac{58}{39997}, the coefficient of the x term, by 2 to get -\frac{29}{39997}. Then add the square of -\frac{29}{39997} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$M^{2}-\frac{58}{39997}M+\left(-\frac{29}{39997}\right)^{2}=\left(-\frac{29}{39997}\right)^{2}$$

Square -\frac{29}{39997} by squaring both the numerator and the denominator of the fraction.

$$M^{2}-\frac{58}{39997}M+\frac{841}{1599760009}=\frac{841}{1599760009}$$

Factor M^{2}-\frac{58}{39997}M+\frac{841}{1599760009}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(M-\frac{29}{39997}\right)^{2}=\frac{841}{1599760009}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(M-\frac{29}{39997}\right)^{2}}=\sqrt{\frac{841}{1599760009}}$$

Simplify.

$$M-\frac{29}{39997}=\frac{29}{39997} M-\frac{29}{39997}=-\frac{29}{39997}$$

Add \frac{29}{39997} to both sides of the equation.

$$M=\frac{58}{39997} M=0$$

Variable M cannot be equal to 0.

$$M=\frac{58}{39997}$$