Solve x=60+frac{x/sqrt{3}}{sqrt{3}}

$$x = \frac{ 60+ \frac{ x }{ \sqrt{ 3 } } }{ \sqrt{ 3 } }$$

Solve for x

$$x=30\sqrt{3}\approx 51.961524227$$

Steps for Solving Linear Equation

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

$$x=\frac{60+\frac{x\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{3}}$$

The square of \sqrt{3} is 3.

$$x=\frac{60+\frac{x\sqrt{3}}{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{60+\frac{x\sqrt{3}}{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$x=\frac{\left(60+\frac{x\sqrt{3}}{3}\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$x=\frac{\left(60+\frac{x\sqrt{3}}{3}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 60+\frac{x\sqrt{3}}{3} by \sqrt{3}.

$$x=\frac{60\sqrt{3}+\frac{x\sqrt{3}}{3}\sqrt{3}}{3}$$

Express \frac{x\sqrt{3}}{3}\sqrt{3} as a single fraction.

$$x=\frac{60\sqrt{3}+\frac{x\sqrt{3}\sqrt{3}}{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$x=\frac{60\sqrt{3}+\frac{x\times 3}{3}}{3}$$

Cancel out 3 and 3.

$$x=\frac{60\sqrt{3}+x}{3}$$

Divide each term of 60\sqrt{3}+x by 3 to get 20\sqrt{3}+\frac{1}{3}x.

$$x=20\sqrt{3}+\frac{1}{3}x$$

Subtract \frac{1}{3}x from both sides.

$$x-\frac{1}{3}x=20\sqrt{3}$$

Combine x and -\frac{1}{3}x to get \frac{2}{3}x.

$$\frac{2}{3}x=20\sqrt{3}$$

Divide both sides of the equation by \frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{3}x}{\frac{2}{3}}=\frac{20\sqrt{3}}{\frac{2}{3}}$$

Dividing by \frac{2}{3} undoes the multiplication by \frac{2}{3}.

$$x=\frac{20\sqrt{3}}{\frac{2}{3}}$$

Divide 20\sqrt{3} by \frac{2}{3} by multiplying 20\sqrt{3} by the reciprocal of \frac{2}{3}.

$$x=30\sqrt{3}$$