Solve x+15=frac{sqrt{2}}{3}x+15sqrt{3}

$$x + 15 = \frac { \sqrt { 2 } } { 3 } x + 15 \sqrt { 3 }$$

Solve for x

$$x = \frac{45 {(\sqrt{6} + 3 \sqrt{3} - \sqrt{2} - 3)}}{7} \approx 20.773469591$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3x+45=\sqrt{2}x+45\sqrt{3}$$

Subtract \sqrt{2}x from both sides.

$$3x+45-\sqrt{2}x=45\sqrt{3}$$

Subtract 45 from both sides.

$$3x-\sqrt{2}x=45\sqrt{3}-45$$

Combine all terms containing x.

$$\left(3-\sqrt{2}\right)x=45\sqrt{3}-45$$

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

$$\frac{\left(3-\sqrt{2}\right)x}{3-\sqrt{2}}=\frac{45\sqrt{3}-45}{3-\sqrt{2}}$$

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

$$x=\frac{45\sqrt{3}-45}{3-\sqrt{2}}$$

Divide 45\sqrt{3}-45 by 3-\sqrt{2}.

$$x=\frac{45\sqrt{6}+135\sqrt{3}-45\sqrt{2}-135}{7}$$