Solve x=frac{sqrt{5y+150}}{5}+3

$$x = \frac { \sqrt { 5 y + 150 } } { 5 } + 3$$

Solve for y

$$y=5\left(x^{2}-6x+3\right)$$

$$5x-15\geq 0$$

Steps for Solving Radical Equations

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

$$\frac{\sqrt{5y+150}}{5}+3=x$$

Subtract 3 from both sides.

$$\frac{\sqrt{5y+150}}{5}=x-3$$

Multiply both sides of the equation by 5.

$$\sqrt{5y+150}=5x-15$$

Square both sides of the equation.

$$5y+150=25\left(x-3\right)^{2}$$

Subtract 150 from both sides of the equation.

$$5y+150-150=25\left(x-3\right)^{2}-150$$

Subtracting 150 from itself leaves 0.

$$5y=25\left(x-3\right)^{2}-150$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{25\left(x-3\right)^{2}-150}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{25\left(x-3\right)^{2}-150}{5}$$

Divide 25\left(-3+x\right)^{2}-150 by 5.

$$y=5\left(x-3\right)^{2}-30$$

Solve for x (complex solution)

$$x=\frac{\sqrt{5\left(y+30\right)}+15}{5}$$

Solve for y (complex solution)

$$y=5\left(x^{2}-6x+3\right)$$

$$x=3\text{ or }arg(15-5x)\geq \pi$$

Solve for x

$$x=\frac{\sqrt{5\left(y+30\right)}+15}{5}$$

$$y\geq -30$$