Solve y=sqrt{x-3y}

$$y = \sqrt { x - 3 y }$$

Solve for x

$$x=y\left(y+3\right)$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{x-3y}=y$$

Square both sides of the equation.

$$x-3y=y^{2}$$

Subtract -3y from both sides of the equation.

$$x-3y-\left(-3y\right)=y^{2}-\left(-3y\right)$$

Subtracting -3y from itself leaves 0.

$$x=y^{2}-\left(-3y\right)$$

Subtract -3y from y^{2}.

$$x=y\left(y+3\right)$$

Solve for x (complex solution)

$$x=y\left(y+3\right)$$

$$arg(y)<\pi \text{ or }y=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{\sqrt{4x+9}-3}{2}\text{, }&arg(\frac{\sqrt{4x+9}-3}{2})<\pi \text{ or }x=0\\y=\frac{-\sqrt{4x+9}-3}{2}\text{, }&arg(\frac{-\sqrt{4x+9}-3}{2})<\pi \end{matrix}\right.$$

Solve for y

$$y=\frac{\sqrt{4x+9}-3}{2}$$

$$x\geq 0$$