Solve 100sqrt{3}+sqrt{3}x=4x

$$100 \sqrt{ 3 } + \sqrt{ 3 } x=4x$$

Solve for x

$$x = \frac{400 \sqrt{3} + 300}{13} \approx 76.370794079$$

Steps for Solving Linear Equation

Subtract 4x from both sides.

$$100\sqrt{3}+\sqrt{3}x-4x=0$$

Subtract 100\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{3}x-4x=-100\sqrt{3}$$

Combine all terms containing x.

$$\left(\sqrt{3}-4\right)x=-100\sqrt{3}$$

Divide both sides by \sqrt{3}-4.

$$\frac{\left(\sqrt{3}-4\right)x}{\sqrt{3}-4}=-\frac{100\sqrt{3}}{\sqrt{3}-4}$$

Dividing by \sqrt{3}-4 undoes the multiplication by \sqrt{3}-4.

$$x=-\frac{100\sqrt{3}}{\sqrt{3}-4}$$

Divide -100\sqrt{3} by \sqrt{3}-4.

$$x=\frac{400\sqrt{3}+300}{13}$$