Solve y=5+sqrt{3x-6}

$$y=5+ \sqrt{ 3x-6 }$$

Solve for x

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

$$y-5\geq 0$$

Steps for Solving Radical Equations

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

$$5+\sqrt{3x-6}=y$$

Subtract 5 from both sides.

$$\sqrt{3x-6}=y-5$$

Square both sides of the equation.

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

Add 6 to both sides of the equation.

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

Subtracting -6 from itself leaves 0.

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

Subtract -6 from \left(y-5\right)^{2}.

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

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Divide \left(y-5\right)^{2}+6 by 3.

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

Solve for x (complex solution)

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

$$y=5\text{ or }arg(5-y)\geq \pi$$

Solve for y (complex solution)

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

Solve for y

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

$$x\geq 2$$