Solve 5x^2=-6

$$5 x ^ { 2 } = - 6$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{30}i}{5}\approx -0-1.095445115i$$

$$x=\frac{\sqrt{30}i}{5}\approx 1.095445115i$$

Steps by Finding Square Root

Divide both sides by 5.

$$x^{2}=-\frac{6}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{30}i}{5} x=-\frac{\sqrt{30}i}{5}$$

Steps Using the Quadratic Formula

Divide both sides by 5.

$$x^{2}=-\frac{6}{5}$$

Add \frac{6}{5} to both sides.

$$x^{2}+\frac{6}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and \frac{6}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{6}{5}}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{6}{5}}}{2}$$

Multiply -4 times \frac{6}{5}.

$$x=\frac{0±\sqrt{-\frac{24}{5}}}{2}$$

Take the square root of -\frac{24}{5}.

$$x=\frac{0±\frac{2\sqrt{30}i}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{30}i}{5}}{2} when ± is plus.

$$x=\frac{\sqrt{30}i}{5}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{30}i}{5}}{2} when ± is minus.

$$x=-\frac{\sqrt{30}i}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{30}i}{5} x=-\frac{\sqrt{30}i}{5}$$