Solve 108+x^2/4=x^2

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

Solve for x

$$x=6$$

$$x=-6$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$108+x^{2}=4x^{2}$$

Subtract 4x^{2} from both sides.

$$108+x^{2}-4x^{2}=0$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$108-3x^{2}=0$$

Subtract 108 from both sides. Anything subtracted from zero gives its negation.

$$-3x^{2}=-108$$

Divide both sides by -3.

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

Divide -108 by -3 to get 36.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$108+x^{2}=4x^{2}$$

Subtract 4x^{2} from both sides.

$$108+x^{2}-4x^{2}=0$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$108-3x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-3x^{2}+108=0$$

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

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

Square 0.

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

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 108}}{2\left(-3\right)}$$

Multiply 12 times 108.

$$x=\frac{0±\sqrt{1296}}{2\left(-3\right)}$$

Take the square root of 1296.

$$x=\frac{0±36}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±36}{-6}$$

Now solve the equation x=\frac{0±36}{-6} when ± is plus. Divide 36 by -6.

$$x=-6$$

Now solve the equation x=\frac{0±36}{-6} when ± is minus. Divide -36 by -6.

$$x=6$$

The equation is now solved.

$$x=-6 x=6$$