Solve 75/2x=2x/3

$$\frac { 75 } { 2 x } = \frac { 2 x } { 3 }$$

Solve for x

$$x = -\frac{15}{2} = -7\frac{1}{2} = -7.5$$

$$x = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6x, the least common multiple of 2x,3.

$$3\times 75=2x\times 2x$$

Multiply 2x and 2x to get \left(2x\right)^{2}.

$$3\times 75=\left(2x\right)^{2}$$

Multiply 3 and 75 to get 225.

$$225=\left(2x\right)^{2}$$

Expand \left(2x\right)^{2}.

$$225=2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$225=4x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}=225$$

Divide both sides by 4.

$$x^{2}=\frac{225}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{15}{2} x=-\frac{15}{2}$$

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 6x, the least common multiple of 2x,3.

$$3\times 75=2x\times 2x$$

Multiply 2x and 2x to get \left(2x\right)^{2}.

$$3\times 75=\left(2x\right)^{2}$$

Multiply 3 and 75 to get 225.

$$225=\left(2x\right)^{2}$$

Expand \left(2x\right)^{2}.

$$225=2^{2}x^{2}$$

Calculate 2 to the power of 2 and get 4.

$$225=4x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$4x^{2}=225$$

Subtract 225 from both sides.

$$4x^{2}-225=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -225 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-225\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-225\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-225\right)}}{2\times 4}$$

Multiply -16 times -225.

$$x=\frac{0±\sqrt{3600}}{2\times 4}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±60}{8}$$

Now solve the equation x=\frac{0±60}{8} when ± is plus. Reduce the fraction \frac{60}{8} to lowest terms by extracting and canceling out 4.

$$x=\frac{15}{2}$$

Now solve the equation x=\frac{0±60}{8} when ± is minus. Reduce the fraction \frac{-60}{8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{15}{2}$$

The equation is now solved.

$$x=\frac{15}{2} x=-\frac{15}{2}$$