Solve 3x*1/4x=108

$$3 x \cdot \frac { 1 } { 4 } x = 108$$

Solve for x

$$x=12$$

$$x=-12$$

Steps by Finding Square Root

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

$$3x^{2}\times \frac{1}{4}=108$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{3}{4}x^{2}=108$$

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

$$x^{2}=108\times \frac{4}{3}$$

Express 108\times \frac{4}{3} as a single fraction.

$$x^{2}=\frac{108\times 4}{3}$$

Multiply 108 and 4 to get 432.

$$x^{2}=\frac{432}{3}$$

Divide 432 by 3 to get 144.

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

Steps Using the Quadratic Formula

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

$$3x^{2}\times \frac{1}{4}=108$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{3}{4}x^{2}=108$$

Subtract 108 from both sides.

$$\frac{3}{4}x^{2}-108=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3}{4} for a, 0 for b, and -108 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3}{4}\left(-108\right)}}{2\times \frac{3}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3}{4}\left(-108\right)}}{2\times \frac{3}{4}}$$

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

$$x=\frac{0±\sqrt{-3\left(-108\right)}}{2\times \frac{3}{4}}$$

Multiply -3 times -108.

$$x=\frac{0±\sqrt{324}}{2\times \frac{3}{4}}$$

Take the square root of 324.

$$x=\frac{0±18}{2\times \frac{3}{4}}$$

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

$$x=\frac{0±18}{\frac{3}{2}}$$

Now solve the equation x=\frac{0±18}{\frac{3}{2}} when ± is plus. Divide 18 by \frac{3}{2} by multiplying 18 by the reciprocal of \frac{3}{2}.

$$x=12$$

Now solve the equation x=\frac{0±18}{\frac{3}{2}} when ± is minus. Divide -18 by \frac{3}{2} by multiplying -18 by the reciprocal of \frac{3}{2}.

$$x=-12$$

The equation is now solved.

$$x=12 x=-12$$