Solve 5+sqrt{3y}=2x+sqrt{3}-y

$$5+ \sqrt{ 3y } =2x+ \sqrt{ 3 } -y$$

Solve for x (complex solution)

$$x=\frac{y+\sqrt{3y}+5-\sqrt{3}}{2}$$

Steps for Solving Linear Equation

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

$$2x+\sqrt{3}-y=5+\sqrt{3y}$$

Subtract \sqrt{3} from both sides.

$$2x-y=5+\sqrt{3y}-\sqrt{3}$$

Add y to both sides.

$$2x=5+\sqrt{3y}-\sqrt{3}+y$$

The equation is in standard form.

$$2x=y+\sqrt{3y}+5-\sqrt{3}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{y+\sqrt{3y}+5-\sqrt{3}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{y+\sqrt{3y}+5-\sqrt{3}}{2}$$

Solve for x

$$x=\frac{y+\sqrt{3y}+5-\sqrt{3}}{2}$$

$$y\geq 0$$

Steps for Solving Linear Equation

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

$$2x+\sqrt{3}-y=5+\sqrt{3y}$$

Subtract \sqrt{3} from both sides.

$$2x-y=5+\sqrt{3y}-\sqrt{3}$$

Add y to both sides.

$$2x=5+\sqrt{3y}-\sqrt{3}+y$$

The equation is in standard form.

$$2x=y+\sqrt{3y}+5-\sqrt{3}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{y+\sqrt{3y}+5-\sqrt{3}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{y+\sqrt{3y}+5-\sqrt{3}}{2}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=2x+\frac{\sqrt{24x+12\sqrt{3}-51}}{2}+\sqrt{3}-\frac{7}{2}\text{, }&arg(\frac{-\sqrt{8x+4\sqrt{3}-17}-\sqrt{3}}{2})<\pi \\y=2x-\frac{\sqrt{24x+12\sqrt{3}-51}}{2}+\sqrt{3}-\frac{7}{2}\text{, }&arg(\frac{\sqrt{8x+4\sqrt{3}-17}-\sqrt{3}}{2})<\pi \text{ or }x=\frac{5-\sqrt{3}}{2}\end{matrix}\right.$$

Solve for y

$$y=2x-\frac{\sqrt{24x+12\sqrt{3}-51}}{2}+\sqrt{3}-\frac{7}{2}$$

$$x\geq \frac{5-\sqrt{3}}{2}$$