Solve y=sqrt{6x-7}

$$y = \sqrt{ 6x-7 }$$

Solve for x

$$x=\frac{y^{2}+7}{6}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{6x-7}=y$$

Square both sides of the equation.

$$6x-7=y^{2}$$

Add 7 to both sides of the equation.

$$6x-7-\left(-7\right)=y^{2}-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$6x=y^{2}-\left(-7\right)$$

Subtract -7 from y^{2}.

$$6x=y^{2}+7$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{y^{2}+7}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{y^{2}+7}{6}$$

Solve for x (complex solution)

$$x=\frac{y^{2}+7}{6}$$

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

Solve for y

$$y=\sqrt{6x-7}$$

$$x\geq \frac{7}{6}$$