Solve sqrt{3}x-8(-frac{sqrt{2}x}{sqrt{3}})=0

$$\sqrt { 3 } x - 8 ( - \frac { \sqrt { 2 } x } { \sqrt { 3 } } ) = 0$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{\sqrt{2}x}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{3}x-8\left(-\frac{\sqrt{2}x\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)=0$$

The square of \sqrt{3} is 3.

$$\sqrt{3}x-8\left(-\frac{\sqrt{2}x\sqrt{3}}{3}\right)=0$$

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

$$\sqrt{3}x-8\left(-\frac{\sqrt{6}x}{3}\right)=0$$

Express 8\left(-\frac{\sqrt{6}x}{3}\right) as a single fraction.

$$\sqrt{3}x-\frac{-8\sqrt{6}x}{3}=0$$

Multiply both sides of the equation by 3.

$$3\sqrt{3}x+8\sqrt{6}x=0$$

Combine all terms containing x.

$$\left(3\sqrt{3}+8\sqrt{6}\right)x=0$$

Divide 0 by 3\sqrt{3}+8\sqrt{6}.

$$x=0$$