Solve y=sqrt{5-9x}

$$y = \sqrt { 5 - 9 x }$$

Solve for x

$$x=\frac{5-y^{2}}{9}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{5-9x}=y$$

Square both sides of the equation.

$$-9x+5=y^{2}$$

Subtract 5 from both sides of the equation.

$$-9x+5-5=y^{2}-5$$

Subtracting 5 from itself leaves 0.

$$-9x=y^{2}-5$$

Divide both sides by -9.

$$\frac{-9x}{-9}=\frac{y^{2}-5}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$x=\frac{y^{2}-5}{-9}$$

Divide y^{2}-5 by -9.

$$x=\frac{5-y^{2}}{9}$$

Solve for x (complex solution)

$$x=\frac{5-y^{2}}{9}$$

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

Solve for y

$$y=\sqrt{5-9x}$$

$$x\leq \frac{5}{9}$$