Solve 8/x=-24x=

$$\frac { 8 } { x } = - 24 x =$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3}i}{3}\approx -0-0.577350269i$$

$$x=\frac{\sqrt{3}i}{3}\approx 0.577350269i$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$8=-24xx$$

Multiply x and x to get x^{2}.

$$8=-24x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-24x^{2}=8$$

Divide both sides by -24.

$$x^{2}=\frac{8}{-24}$$

Reduce the fraction \frac{8}{-24} to lowest terms by extracting and canceling out 8.

$$x^{2}=-\frac{1}{3}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$8=-24xx$$

Multiply x and x to get x^{2}.

$$8=-24x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$-24x^{2}=8$$

Subtract 8 from both sides.

$$-24x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -24 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-24\right)\left(-8\right)}}{2\left(-24\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-24\right)\left(-8\right)}}{2\left(-24\right)}$$

Multiply -4 times -24.

$$x=\frac{0±\sqrt{96\left(-8\right)}}{2\left(-24\right)}$$

Multiply 96 times -8.

$$x=\frac{0±\sqrt{-768}}{2\left(-24\right)}$$

Take the square root of -768.

$$x=\frac{0±16\sqrt{3}i}{2\left(-24\right)}$$

Multiply 2 times -24.

$$x=\frac{0±16\sqrt{3}i}{-48}$$

Now solve the equation x=\frac{0±16\sqrt{3}i}{-48} when ± is plus.

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

Now solve the equation x=\frac{0±16\sqrt{3}i}{-48} when ± is minus.

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

The equation is now solved.

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