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

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

Solve for x

$$x=2\sqrt{3}\left(\sqrt{6}-2\right)\approx 1.557078144$$

Steps for Solving Linear Equation

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

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

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

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

Add \sqrt{3}x to both sides.

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

Add \sqrt{6} to both sides.

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

Combine \sqrt{6} and \sqrt{6} to get 2\sqrt{6}.

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

Combine all terms containing x.

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

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

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

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

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

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

$$x=6\sqrt{2}-4\sqrt{3}$$