Solve y-3/2=sqrt{3}(x-5/3)

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

Solve for x

$$x=\frac{\sqrt{3}\left(2y-3\right)+10}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{3} by x-\frac{5}{3}.

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

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

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

Add \frac{5}{3}\sqrt{3} to both sides.

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

The equation is in standard form.

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

Divide both sides by \sqrt{3}.

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

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

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

Divide y-\frac{3}{2}+\frac{5\sqrt{3}}{3} by \sqrt{3}.

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

Solve for y

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