Solve x/y+5y=0

$$\frac{ x }{ y } +5y=0$$

Solve for x

$$x=-5y^{2}$$

$$y\neq 0$$

Solution Steps

Multiply both sides of the equation by y.

$$x+5yy=0$$

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

$$x+5y^{2}=0$$

Subtract 5y^{2} from both sides. Anything subtracted from zero gives its negation.

$$x=-5y^{2}$$

Solve for y (complex solution)

$$y=-\frac{i\sqrt{5x}}{5}$$

$$y=\frac{i\sqrt{5x}}{5}\text{, }x\neq 0$$

Solve for y

$$y=\frac{\sqrt{-5x}}{5}$$

$$y=-\frac{\sqrt{-5x}}{5}\text{, }x<0$$