Solve sqrt{3}x+sqrt{5}=3x

$$\sqrt { 3 } x + \sqrt { 5 } = 3 x$$

Solve for x

$$x = \frac{\sqrt{15} + 3 \sqrt{5}}{6} \approx 1.763531213$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

$$\sqrt{3}x+\sqrt{5}-3x=0$$

Subtract \sqrt{5} from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{3}x-3x=-\sqrt{5}$$

Combine all terms containing x.

$$\left(\sqrt{3}-3\right)x=-\sqrt{5}$$

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

$$\frac{\left(\sqrt{3}-3\right)x}{\sqrt{3}-3}=-\frac{\sqrt{5}}{\sqrt{3}-3}$$

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

$$x=-\frac{\sqrt{5}}{\sqrt{3}-3}$$

Divide -\sqrt{5} by \sqrt{3}-3.

$$x=\frac{\sqrt{5}}{2}+\frac{\sqrt{15}}{6}$$