Solve x=(12+x)divsqrt{3}

$$x=(12+x) \div \sqrt{ 3 }$$

Solve for x

$$x=6\left(\sqrt{3}+1\right)\approx 16.392304845$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{12+x}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$x=\frac{\left(12+x\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$x=\frac{\left(12+x\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 12+x by \sqrt{3}.

$$x=\frac{12\sqrt{3}+x\sqrt{3}}{3}$$

Subtract \frac{12\sqrt{3}+x\sqrt{3}}{3} from both sides.

$$x-\frac{12\sqrt{3}+x\sqrt{3}}{3}=0$$

Multiply both sides of the equation by 3.

$$3x-\left(12\sqrt{3}+x\sqrt{3}\right)=0$$

To find the opposite of 12\sqrt{3}+x\sqrt{3}, find the opposite of each term.

$$3x-12\sqrt{3}-x\sqrt{3}=0$$

Add 12\sqrt{3} to both sides. Anything plus zero gives itself.

$$3x-x\sqrt{3}=12\sqrt{3}$$

Combine all terms containing x.

$$\left(3-\sqrt{3}\right)x=12\sqrt{3}$$

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

$$\frac{\left(3-\sqrt{3}\right)x}{3-\sqrt{3}}=\frac{12\sqrt{3}}{3-\sqrt{3}}$$

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

$$x=\frac{12\sqrt{3}}{3-\sqrt{3}}$$

Divide 12\sqrt{3} by 3-\sqrt{3}.

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