Solve sqrt{3}(x-20)=40+x

$$\sqrt { 3 } ( x - 20 ) = 40 + x$$

Solve for x

$$x=30\sqrt{3}+50\approx 101.961524227$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{3} by x-20.

$$\sqrt{3}x-20\sqrt{3}=40+x$$

Subtract x from both sides.

$$\sqrt{3}x-20\sqrt{3}-x=40$$

Add 20\sqrt{3} to both sides.

$$\sqrt{3}x-x=40+20\sqrt{3}$$

Combine all terms containing x.

$$\left(\sqrt{3}-1\right)x=40+20\sqrt{3}$$

The equation is in standard form.

$$\left(\sqrt{3}-1\right)x=20\sqrt{3}+40$$

Divide both sides by \sqrt{3}-1.

$$\frac{\left(\sqrt{3}-1\right)x}{\sqrt{3}-1}=\frac{20\sqrt{3}+40}{\sqrt{3}-1}$$

Dividing by \sqrt{3}-1 undoes the multiplication by \sqrt{3}-1.

$$x=\frac{20\sqrt{3}+40}{\sqrt{3}-1}$$

Divide 40+20\sqrt{3} by \sqrt{3}-1.

$$x=30\sqrt{3}+50$$