Solve 8-12x^2=0

$$8-12 { x }^{ 2 } =0$$

Solve for x

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$-12x^{2}=-8$$

Divide both sides by -12.

$$x^{2}=\frac{-8}{-12}$$

Reduce the fraction \frac{-8}{-12} to lowest terms by extracting and canceling out -4.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

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.

$$-12x^{2}+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -12 for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12\right)\times 8}}{2\left(-12\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-12\right)\times 8}}{2\left(-12\right)}$$

Multiply -4 times -12.

$$x=\frac{0±\sqrt{48\times 8}}{2\left(-12\right)}$$

Multiply 48 times 8.

$$x=\frac{0±\sqrt{384}}{2\left(-12\right)}$$

Take the square root of 384.

$$x=\frac{0±8\sqrt{6}}{2\left(-12\right)}$$

Multiply 2 times -12.

$$x=\frac{0±8\sqrt{6}}{-24}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{-24} when ± is plus.

$$x=-\frac{\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±8\sqrt{6}}{-24} when ± is minus.

$$x=\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$x=-\frac{\sqrt{6}}{3} x=\frac{\sqrt{6}}{3}$$