Solve 3/x=-1/3x

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

Solve for x (complex solution)

$$x=-3i$$

$$x=3i$$

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 3x, the least common multiple of x,3.

$$3\times 3=-\frac{1}{3}x\times 3x$$

Multiply 3 and 3 to get 9.

$$9=-\frac{1}{3}x\times 3x$$

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

$$9=-\frac{1}{3}x^{2}\times 3$$

Cancel out 3 and 3.

$$9=-x^{2}$$

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

$$-x^{2}=9$$

Divide both sides by -1.

$$x^{2}=-9$$

The equation is now solved.

$$x=3i x=-3i$$

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 3x, the least common multiple of x,3.

$$3\times 3=-\frac{1}{3}x\times 3x$$

Multiply 3 and 3 to get 9.

$$9=-\frac{1}{3}x\times 3x$$

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

$$9=-\frac{1}{3}x^{2}\times 3$$

Cancel out 3 and 3.

$$9=-x^{2}$$

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

$$-x^{2}=9$$

Subtract 9 from both sides.

$$-x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-9\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-9\right)}}{2\left(-1\right)}$$

Multiply 4 times -9.

$$x=\frac{0±\sqrt{-36}}{2\left(-1\right)}$$

Take the square root of -36.

$$x=\frac{0±6i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±6i}{-2}$$

Now solve the equation x=\frac{0±6i}{-2} when ± is plus.

$$x=-3i$$

Now solve the equation x=\frac{0±6i}{-2} when ± is minus.

$$x=3i$$

The equation is now solved.

$$x=-3i x=3i$$