Solve 3/2=1/4x^2

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

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

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

Multiply \frac{3}{2} and 4 to get 6.

$$6=x^{2}$$

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

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

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

Multiply \frac{3}{2} and 4 to get 6.

$$6=x^{2}$$

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

$$x^{2}=6$$

Subtract 6 from both sides.

$$x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)}}{2}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24}}{2}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{2} when ± is plus.

$$x=\sqrt{6}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{2} when ± is minus.

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$