Solve frac{2xsqrt{3}}{3}+xsqrt{2}=100

$$\frac{ 2x \sqrt{ 3 } }{ 3 } +x \sqrt{ 2 } =100$$

Solve for x

$$x=50\sqrt{3}\left(\sqrt{6}-2\right)\approx 38.926953599$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$2x\sqrt{3}+3x\sqrt{2}=300$$

Combine all terms containing x.

$$\left(2\sqrt{3}+3\sqrt{2}\right)x=300$$

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

$$\frac{\left(2\sqrt{3}+3\sqrt{2}\right)x}{2\sqrt{3}+3\sqrt{2}}=\frac{300}{2\sqrt{3}+3\sqrt{2}}$$

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

$$x=\frac{300}{2\sqrt{3}+3\sqrt{2}}$$

Divide 300 by 2\sqrt{3}+3\sqrt{2}.

$$x=150\sqrt{2}-100\sqrt{3}$$