Solve 3/4x*x=192

$$\frac{ 3 }{ 4 } x \times x=192$$

Solve for x

$$x=16$$

$$x=-16$$

Steps by Finding Square Root

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

$$\frac{3}{4}x^{2}=192$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$x^{2}=192\times \frac{4}{3}$$

Express 192\times \frac{4}{3} as a single fraction.

$$x^{2}=\frac{192\times 4}{3}$$

Multiply 192 and 4 to get 768.

$$x^{2}=\frac{768}{3}$$

Divide 768 by 3 to get 256.

$$x^{2}=256$$

Take the square root of both sides of the equation.

$$x=16 x=-16$$

Steps Using the Quadratic Formula

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

$$\frac{3}{4}x^{2}=192$$

Subtract 192 from both sides.

$$\frac{3}{4}x^{2}-192=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{4} for a, 0 for b, and -192 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{4}\left(-192\right)}}{2\times \frac{3}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{4}\left(-192\right)}}{2\times \frac{3}{4}}$$

Multiply -4 times \frac{3}{4}.

$$x=\frac{0±\sqrt{-3\left(-192\right)}}{2\times \frac{3}{4}}$$

Multiply -3 times -192.

$$x=\frac{0±\sqrt{576}}{2\times \frac{3}{4}}$$

Take the square root of 576.

$$x=\frac{0±24}{2\times \frac{3}{4}}$$

Multiply 2 times \frac{3}{4}.

$$x=\frac{0±24}{\frac{3}{2}}$$

Now solve the equation x=\frac{0±24}{\frac{3}{2}} when ± is plus. Divide 24 by \frac{3}{2} by multiplying 24 by the reciprocal of \frac{3}{2}.

$$x=16$$

Now solve the equation x=\frac{0±24}{\frac{3}{2}} when ± is minus. Divide -24 by \frac{3}{2} by multiplying -24 by the reciprocal of \frac{3}{2}.

$$x=-16$$

The equation is now solved.

$$x=16 x=-16$$