Solve y=sqrt{9-3x}

$$y = \sqrt { 9 - 3 x }$$

Solve for x

$$x=-\frac{y^{2}}{3}+3$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{9-3x}=y$$

Square both sides of the equation.

$$-3x+9=y^{2}$$

Subtract 9 from both sides of the equation.

$$-3x+9-9=y^{2}-9$$

Subtracting 9 from itself leaves 0.

$$-3x=y^{2}-9$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{y^{2}-9}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{y^{2}-9}{-3}$$

Divide y^{2}-9 by -3.

$$x=-\frac{y^{2}}{3}+3$$

Solve for x (complex solution)

$$x=-\frac{y^{2}}{3}+3$$

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

Solve for y

$$y=\sqrt{9-3x}$$

$$x\leq 3$$