Solve y=6sqrt{5+7x}

$$y = 6 \sqrt { 5 + 7 x }$$

Solve for x

$$x=\frac{y^{2}-180}{252}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$6\sqrt{5+7x}=y$$

Divide both sides by 6.

$$\frac{6\sqrt{7x+5}}{6}=\frac{y}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$\sqrt{7x+5}=\frac{y}{6}$$

Square both sides of the equation.

$$7x+5=\frac{y^{2}}{36}$$

Subtract 5 from both sides of the equation.

$$7x+5-5=\frac{y^{2}}{36}-5$$

Subtracting 5 from itself leaves 0.

$$7x=\frac{y^{2}}{36}-5$$

Divide both sides by 7.

$$\frac{7x}{7}=\frac{\frac{y^{2}}{36}-5}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x=\frac{\frac{y^{2}}{36}-5}{7}$$

Divide \frac{y^{2}}{36}-5 by 7.

$$x=\frac{y^{2}}{252}-\frac{5}{7}$$

Solve for x (complex solution)

$$x=\frac{y^{2}-180}{252}$$

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

Solve for y (complex solution)

$$y=6\sqrt{7x+5}$$

Solve for y

$$y=6\sqrt{7x+5}$$

$$x\geq -\frac{5}{7}$$