Solve 4/15x+2.8=63-3/20x

$$\frac{ 4 }{ 15 } x+2.8=63- \frac{ 3 }{ 20x }$$

Solve for x

$$x = \frac{3 \sqrt{90597} + 903}{8} \approx 225.747508278$$

$$x=\frac{903-3\sqrt{90597}}{8}\approx 0.002491722$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 60x, the least common multiple of 15,20x.

$$\frac{4}{15}x\times 60x+60x\times 2.8=60x\times 63-3\times 3$$

Multiply \frac{4}{15} and 60 to get 16.

$$16xx+60x\times 2.8=60x\times 63-3\times 3$$

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

$$16x^{2}+60x\times 2.8=60x\times 63-3\times 3$$

Multiply 60 and 2.8 to get 168.

$$16x^{2}+168x=60x\times 63-3\times 3$$

Multiply 60 and 63 to get 3780.

$$16x^{2}+168x=3780x-3\times 3$$

Multiply -3 and 3 to get -9.

$$16x^{2}+168x=3780x-9$$

Subtract 3780x from both sides.

$$16x^{2}+168x-3780x=-9$$

Combine 168x and -3780x to get -3612x.

$$16x^{2}-3612x=-9$$

Add 9 to both sides.

$$16x^{2}-3612x+9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, -3612 for b, and 9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3612\right)±\sqrt{\left(-3612\right)^{2}-4\times 16\times 9}}{2\times 16}$$

Square -3612.

$$x=\frac{-\left(-3612\right)±\sqrt{13046544-4\times 16\times 9}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{-\left(-3612\right)±\sqrt{13046544-64\times 9}}{2\times 16}$$

Multiply -64 times 9.

$$x=\frac{-\left(-3612\right)±\sqrt{13046544-576}}{2\times 16}$$

Add 13046544 to -576.

$$x=\frac{-\left(-3612\right)±\sqrt{13045968}}{2\times 16}$$

Take the square root of 13045968.

$$x=\frac{-\left(-3612\right)±12\sqrt{90597}}{2\times 16}$$

The opposite of -3612 is 3612.

$$x=\frac{3612±12\sqrt{90597}}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{3612±12\sqrt{90597}}{32}$$

Now solve the equation x=\frac{3612±12\sqrt{90597}}{32} when ± is plus. Add 3612 to 12\sqrt{90597}.

$$x=\frac{12\sqrt{90597}+3612}{32}$$

Divide 3612+12\sqrt{90597} by 32.

$$x=\frac{3\sqrt{90597}+903}{8}$$

Now solve the equation x=\frac{3612±12\sqrt{90597}}{32} when ± is minus. Subtract 12\sqrt{90597} from 3612.

$$x=\frac{3612-12\sqrt{90597}}{32}$$

Divide 3612-12\sqrt{90597} by 32.

$$x=\frac{903-3\sqrt{90597}}{8}$$

The equation is now solved.

$$x=\frac{3\sqrt{90597}+903}{8} x=\frac{903-3\sqrt{90597}}{8}$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 60x, the least common multiple of 15,20x.

$$\frac{4}{15}x\times 60x+60x\times 2.8=60x\times 63-3\times 3$$

Multiply \frac{4}{15} and 60 to get 16.

$$16xx+60x\times 2.8=60x\times 63-3\times 3$$

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

$$16x^{2}+60x\times 2.8=60x\times 63-3\times 3$$

Multiply 60 and 2.8 to get 168.

$$16x^{2}+168x=60x\times 63-3\times 3$$

Multiply 60 and 63 to get 3780.

$$16x^{2}+168x=3780x-3\times 3$$

Multiply -3 and 3 to get -9.

$$16x^{2}+168x=3780x-9$$

Subtract 3780x from both sides.

$$16x^{2}+168x-3780x=-9$$

Combine 168x and -3780x to get -3612x.

$$16x^{2}-3612x=-9$$

Divide both sides by 16.

$$\frac{16x^{2}-3612x}{16}=-\frac{9}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$x^{2}+\left(-\frac{3612}{16}\right)x=-\frac{9}{16}$$

Reduce the fraction \frac{-3612}{16} to lowest terms by extracting and canceling out 4.

$$x^{2}-\frac{903}{4}x=-\frac{9}{16}$$

Divide -\frac{903}{4}, the coefficient of the x term, by 2 to get -\frac{903}{8}. Then add the square of -\frac{903}{8} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{903}{4}x+\left(-\frac{903}{8}\right)^{2}=-\frac{9}{16}+\left(-\frac{903}{8}\right)^{2}$$

Square -\frac{903}{8} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{903}{4}x+\frac{815409}{64}=-\frac{9}{16}+\frac{815409}{64}$$

Add -\frac{9}{16} to \frac{815409}{64} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{903}{4}x+\frac{815409}{64}=\frac{815373}{64}$$

Factor x^{2}-\frac{903}{4}x+\frac{815409}{64}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{903}{8}\right)^{2}=\frac{815373}{64}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{903}{8}\right)^{2}}=\sqrt{\frac{815373}{64}}$$

Simplify.

$$x-\frac{903}{8}=\frac{3\sqrt{90597}}{8} x-\frac{903}{8}=-\frac{3\sqrt{90597}}{8}$$

Add \frac{903}{8} to both sides of the equation.

$$x=\frac{3\sqrt{90597}+903}{8} x=\frac{903-3\sqrt{90597}}{8}$$