Solve 3xsqrt{2}-sqrt{6}=2x

$$3 x \sqrt { 2 } - \sqrt { 6 } = 2 x$$

Solve for x

$$x = \frac{\sqrt{3} {(\sqrt{2} + 3)}}{7} \approx 1.092234595$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$3x\sqrt{2}-\sqrt{6}-2x=0$$

Add \sqrt{6} to both sides. Anything plus zero gives itself.

$$3x\sqrt{2}-2x=\sqrt{6}$$

Combine all terms containing x.

$$\left(3\sqrt{2}-2\right)x=\sqrt{6}$$

Divide both sides by 3\sqrt{2}-2.

$$\frac{\left(3\sqrt{2}-2\right)x}{3\sqrt{2}-2}=\frac{\sqrt{6}}{3\sqrt{2}-2}$$

Dividing by 3\sqrt{2}-2 undoes the multiplication by 3\sqrt{2}-2.

$$x=\frac{\sqrt{6}}{3\sqrt{2}-2}$$

Divide \sqrt{6} by 3\sqrt{2}-2.

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