Solve x/y+5y=10

$$\frac{ x }{ y } +5y=10$$

Solve for x

$$x=-5y\left(y-2\right)$$

$$y\neq 0$$

Solution Steps

Multiply both sides of the equation by y.

$$x+5yy=10y$$

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

$$x+5y^{2}=10y$$

Subtract 5y^{2} from both sides.

$$x=10y-5y^{2}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=\frac{\sqrt{25-5x}}{5}+1\text{, }&\text{unconditionally}\\y=-\frac{\sqrt{25-5x}}{5}+1\text{, }&x\neq 0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{\sqrt{25-5x}}{5}+1\text{, }&x\neq 0\text{ and }x\leq 5\\y=\frac{\sqrt{25-5x}}{5}+1\text{, }&x\leq 5\end{matrix}\right.$$