Solve 9x^2=18xy+9y

$$9 x ^ { 2 } = 18 x y + 9 y$$

Solve for y

$$y=\frac{x^{2}}{2x+1}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

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

$$18xy+9y=9x^{2}$$

Combine all terms containing y.

$$\left(18x+9\right)y=9x^{2}$$

Divide both sides by 18x+9.

$$\frac{\left(18x+9\right)y}{18x+9}=\frac{9x^{2}}{18x+9}$$

Dividing by 18x+9 undoes the multiplication by 18x+9.

$$y=\frac{9x^{2}}{18x+9}$$

Divide 9x^{2} by 18x+9.

$$y=\frac{x^{2}}{2x+1}$$

Solve for x (complex solution)

$$x=\sqrt{y\left(y+1\right)}+y$$

$$x=-\sqrt{y\left(y+1\right)}+y$$

Solve for x

$$x=\sqrt{y\left(y+1\right)}+y$$

$$x=-\sqrt{y\left(y+1\right)}+y\text{, }y\leq -1\text{ or }y\geq 0$$