Solve -3x=12/x

$$- 3 x = \frac { 12 } { x }$$

Solve for x (complex solution)

$$x=2i$$

$$x=-2i$$

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.

$$-3xx=12$$

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

$$-3x^{2}=12$$

Divide both sides by -3.

$$x^{2}=\frac{12}{-3}$$

Divide 12 by -3 to get -4.

$$x^{2}=-4$$

The equation is now solved.

$$x=2i x=-2i$$

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.

$$-3xx=12$$

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

$$-3x^{2}=12$$

Subtract 12 from both sides.

$$-3x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\left(-12\right)}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\left(-12\right)}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\left(-12\right)}}{2\left(-3\right)}$$

Multiply 12 times -12.

$$x=\frac{0±\sqrt{-144}}{2\left(-3\right)}$$

Take the square root of -144.

$$x=\frac{0±12i}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±12i}{-6}$$

Now solve the equation x=\frac{0±12i}{-6} when ± is plus.

$$x=-2i$$

Now solve the equation x=\frac{0±12i}{-6} when ± is minus.

$$x=2i$$

The equation is now solved.

$$x=-2i x=2i$$