Solve x^2+4xy=5y

$$x ^ { 2 } + 4 x y = 5 y$$

Solve for y

$$y=-\frac{x^{2}}{4x-5}$$

$$x\neq \frac{5}{4}$$

Steps for Solving Linear Equation

Subtract 5y from both sides.

$$x^{2}+4xy-5y=0$$

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

$$4xy-5y=-x^{2}$$

Combine all terms containing y.

$$\left(4x-5\right)y=-x^{2}$$

Divide both sides by 4x-5.

$$\frac{\left(4x-5\right)y}{4x-5}=-\frac{x^{2}}{4x-5}$$

Dividing by 4x-5 undoes the multiplication by 4x-5.

$$y=-\frac{x^{2}}{4x-5}$$

Solve for x (complex solution)

$$x=\sqrt{y\left(4y+5\right)}-2y$$

$$x=-\sqrt{y\left(4y+5\right)}-2y$$

Solve for x

$$x=\sqrt{y\left(4y+5\right)}-2y$$

$$x=-\sqrt{y\left(4y+5\right)}-2y\text{, }y\leq -\frac{5}{4}\text{ or }y\geq 0$$