Solve x=frac{sqrt{5y}-15}{5}-3

$$x = \frac{ \sqrt{ 5y } -15 }{ 5 } -3$$

Solve for y

$$y=5\left(x+6\right)^{2}$$

$$x\geq -6$$

Steps for Solving Radical Equations

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

$$\frac{\sqrt{5y}-15}{5}-3=x$$

Add 3 to both sides.

$$\frac{\sqrt{5y}-15}{5}=x+3$$

Multiply both sides of the equation by 5.

$$\sqrt{5y}-15=5x+15$$

Add 15 to both sides.

$$\sqrt{5y}=5x+15+15$$

Add 15 and 15 to get 30.

$$\sqrt{5y}=5x+30$$

Square both sides of the equation.

$$5y=25\left(x+6\right)^{2}$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{25\left(x+6\right)^{2}}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{25\left(x+6\right)^{2}}{5}$$

Divide 25\left(6+x\right)^{2} by 5.

$$y=5\left(x+6\right)^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{5y}-30}{5}$$

Solve for y (complex solution)

$$y=5\left(x+6\right)^{2}$$

$$arg(x+6)<\pi \text{ or }x=-6$$

Solve for x

$$x=\frac{\sqrt{5y}-30}{5}$$

$$y\geq 0$$