Solve 8x^2+0x=-6

$$8 x ^ { 2 } + 0 x = - 6$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3}i}{2}\approx -0-0.866025404i$$

$$x=\frac{\sqrt{3}i}{2}\approx 0.866025404i$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$8x^{2}=-6$$

Add 6 to both sides of the equation.

$$8x^{2}-\left(-6\right)=-6-\left(-6\right)$$

Subtracting -6 from itself leaves 0.

$$8x^{2}-\left(-6\right)=0$$

Subtract -6 from 0.

$$8x^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\times 6}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\times 6}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\times 6}}{2\times 8}$$

Multiply -32 times 6.

$$x=\frac{0±\sqrt{-192}}{2\times 8}$$

Take the square root of -192.

$$x=\frac{0±8\sqrt{3}i}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±8\sqrt{3}i}{16}$$

Now solve the equation x=\frac{0±8\sqrt{3}i}{16} when ± is plus.

$$x=\frac{\sqrt{3}i}{2}$$

Now solve the equation x=\frac{0±8\sqrt{3}i}{16} when ± is minus.

$$x=-\frac{\sqrt{3}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{3}i}{2} x=-\frac{\sqrt{3}i}{2}$$