Solve sqrt{3}left(x-10right)=x

$$\sqrt{ 3 } \left( x-10 \right) = x$$

Solve for x

$$x=5\sqrt{3}+15\approx 23.660254038$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{3} by x-10.

$$\sqrt{3}x-10\sqrt{3}=x$$

Subtract x from both sides.

$$\sqrt{3}x-10\sqrt{3}-x=0$$

Add 10\sqrt{3} to both sides. Anything plus zero gives itself.

$$\sqrt{3}x-x=10\sqrt{3}$$

Combine all terms containing x.

$$\left(\sqrt{3}-1\right)x=10\sqrt{3}$$

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

$$\frac{\left(\sqrt{3}-1\right)x}{\sqrt{3}-1}=\frac{10\sqrt{3}}{\sqrt{3}-1}$$

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

$$x=\frac{10\sqrt{3}}{\sqrt{3}-1}$$

Divide 10\sqrt{3} by \sqrt{3}-1.

$$x=5\sqrt{3}+15$$