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

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

Solve for x

$$x=2\left(\sqrt{3}+1\right)\approx 5.464101615$$

Steps for Solving Linear Equation

Subtract \sqrt{3}x from both sides.

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

Reorder the terms.

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

Combine all terms containing x.

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

The equation is in standard form.

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

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

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

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

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

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

$$x=2\sqrt{3}+2$$