Solve 4x-2sqrt{3}=xsqrt{2}

$$4 x - 2 \sqrt { 3 } = x \sqrt { 2 }$$

Solve for x

$$x = \frac{\sqrt{3} {(\sqrt{2} + 4)}}{7} \approx 1.339670425$$

Steps for Solving Linear Equation

Subtract x\sqrt{2} from both sides.

$$4x-2\sqrt{3}-x\sqrt{2}=0$$

Add 2\sqrt{3} to both sides. Anything plus zero gives itself.

$$4x-x\sqrt{2}=2\sqrt{3}$$

Combine all terms containing x.

$$\left(4-\sqrt{2}\right)x=2\sqrt{3}$$

Divide both sides by 4-\sqrt{2}.

$$\frac{\left(4-\sqrt{2}\right)x}{4-\sqrt{2}}=\frac{2\sqrt{3}}{4-\sqrt{2}}$$

Dividing by 4-\sqrt{2} undoes the multiplication by 4-\sqrt{2}.

$$x=\frac{2\sqrt{3}}{4-\sqrt{2}}$$

Divide 2\sqrt{3} by 4-\sqrt{2}.

$$x=\frac{\sqrt{3}\left(\sqrt{2}+4\right)}{7}$$