Solve 6x^2+90=-6

$$6 x ^ { 2 } + 90 = - 6$$

Solve for x (complex solution)

$$x=-4i$$

$$x=4i$$

Steps by Finding Square Root

Subtract 90 from both sides.

$$6x^{2}=-6-90$$

Subtract 90 from -6 to get -96.

$$6x^{2}=-96$$

Divide both sides by 6.

$$x^{2}=\frac{-96}{6}$$

Divide -96 by 6 to get -16.

$$x^{2}=-16$$

The equation is now solved.

$$x=4i x=-4i$$

Steps Using the Quadratic Formula

Add 6 to both sides.

$$6x^{2}+90+6=0$$

Add 90 and 6 to get 96.

$$6x^{2}+96=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 96 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 96}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\times 96}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 96}}{2\times 6}$$

Multiply -24 times 96.

$$x=\frac{0±\sqrt{-2304}}{2\times 6}$$

Take the square root of -2304.

$$x=\frac{0±48i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±48i}{12}$$

Now solve the equation x=\frac{0±48i}{12} when ± is plus.

$$x=4i$$

Now solve the equation x=\frac{0±48i}{12} when ± is minus.

$$x=-4i$$

The equation is now solved.

$$x=4i x=-4i$$