Solve 5/x=-x/3

$$\frac { 5 } { x } = - \frac { x } { 3 }$$

Solve for x (complex solution)

$$x=-\sqrt{15}i\approx -0-3.872983346i$$

$$x=\sqrt{15}i\approx 3.872983346i$$

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.

$$3\times 5=-xx$$

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

$$3\times 5=-x^{2}$$

Multiply 3 and 5 to get 15.

$$15=-x^{2}$$

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

$$-x^{2}=15$$

Divide both sides by -1.

$$x^{2}=-15$$

The equation is now solved.

$$x=\sqrt{15}i x=-\sqrt{15}i$$

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.

$$3\times 5=-xx$$

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

$$3\times 5=-x^{2}$$

Multiply 3 and 5 to get 15.

$$15=-x^{2}$$

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

$$-x^{2}=15$$

Subtract 15 from both sides.

$$-x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-15\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-15\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-15\right)}}{2\left(-1\right)}$$

Multiply 4 times -15.

$$x=\frac{0±\sqrt{-60}}{2\left(-1\right)}$$

Take the square root of -60.

$$x=\frac{0±2\sqrt{15}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{15}i}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{15}i}{-2} when ± is plus.

$$x=-\sqrt{15}i$$

Now solve the equation x=\frac{0±2\sqrt{15}i}{-2} when ± is minus.

$$x=\sqrt{15}i$$

The equation is now solved.

$$x=-\sqrt{15}i x=\sqrt{15}i$$