Solve 12x^2=-8

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{6}i}{3}\approx -0-0.816496581i$$

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

Steps by Finding Square Root

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.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

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.

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

Add \frac{2}{3} to both sides.

$$x^{2}+\frac{2}{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{2}{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

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

$$x=\frac{0±\sqrt{-\frac{8}{3}}}{2}$$

Take the square root of -\frac{8}{3}.

$$x=\frac{0±\frac{2\sqrt{6}i}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{6}i}{3}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±\frac{2\sqrt{6}i}{3}}{2} when ± is minus.

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

The equation is now solved.

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