Solve x-90=frac{sqrt{3}}{3}x

$$x-90= \frac{ \sqrt{ 3 } }{ 3 } x$$

Solve for x

$$x=45\sqrt{3}+135\approx 212.942286341$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3x-270=\sqrt{3}x$$

Subtract \sqrt{3}x from both sides.

$$3x-270-\sqrt{3}x=0$$

Add 270 to both sides. Anything plus zero gives itself.

$$3x-\sqrt{3}x=270$$

Combine all terms containing x.

$$\left(3-\sqrt{3}\right)x=270$$

Divide both sides by 3-\sqrt{3}.

$$\frac{\left(3-\sqrt{3}\right)x}{3-\sqrt{3}}=\frac{270}{3-\sqrt{3}}$$

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

$$x=\frac{270}{3-\sqrt{3}}$$

Divide 270 by 3-\sqrt{3}.

$$x=45\sqrt{3}+135$$