Solve x=5sqrt{3y+1}

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

Solve for y

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

$$x\geq 0$$

Steps for Solving Radical Equations

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

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

Divide both sides by 5.

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

Dividing by 5 undoes the multiplication by 5.

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

Square both sides of the equation.

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

Subtract 1 from both sides of the equation.

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

Subtracting 1 from itself leaves 0.

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

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

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

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

Solve for y (complex solution)

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

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

Solve for x

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

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