Solve 6x+3sqrt{3}x=2sqrt{2}x+6

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

Solve for x

$$x=\frac{6\left(2\sqrt{2}+3\sqrt{3}-6\right)}{24\sqrt{2}-17}\approx 0.717040747$$

Steps for Solving Linear Equation

Subtract 2\sqrt{2}x from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 6+3\sqrt{3}-2\sqrt{2}.

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

Dividing by 6+3\sqrt{3}-2\sqrt{2} undoes the multiplication by 6+3\sqrt{3}-2\sqrt{2}.

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