Solve sqrt{3}(2-sqrt{3}x)=sqrt{2}

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

Solve for x

$$x=\frac{\sqrt{2}\left(\sqrt{6}-1\right)}{3}\approx 0.683296018$$

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{3} by 2-\sqrt{3}x.

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

The square of \sqrt{3} is 3.

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

Multiply -1 and 3 to get -3.

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

Subtract 2\sqrt{3} from both sides.

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

Divide both sides by -3.

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

Dividing by -3 undoes the multiplication by -3.

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

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

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