Solve y=5sqrt{3x+1}

$$y=5 \sqrt{ 3x+1 }$$

Solve for x

$$x=\frac{y^{2}-25}{75}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$5\sqrt{3x+1}=y$$

Divide both sides by 5.

$$\frac{5\sqrt{3x+1}}{5}=\frac{y}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\sqrt{3x+1}=\frac{y}{5}$$

Square both sides of the equation.

$$3x+1=\frac{y^{2}}{25}$$

Subtract 1 from both sides of the equation.

$$3x+1-1=\frac{y^{2}}{25}-1$$

Subtracting 1 from itself leaves 0.

$$3x=\frac{y^{2}}{25}-1$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{\frac{y^{2}}{25}-1}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{\frac{y^{2}}{25}-1}{3}$$

Divide -1+\frac{y^{2}}{25} by 3.

$$x=\frac{y^{2}}{75}-\frac{1}{3}$$

Solve for x (complex solution)

$$x=\frac{y^{2}-25}{75}$$

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

Solve for y

$$y=5\sqrt{3x+1}$$

$$x\geq -\frac{1}{3}$$