Solve k/-3sqrt{3}+2=2sqrt{3}

$$\frac { k } { - 3 \sqrt { 3 } } + 2 = 2 \sqrt { 3 }$$

Solve for k

$$k=6\left(\sqrt{3}-3\right)\approx -7.607695155$$

Steps for Solving Linear Equation

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

$$\frac{k\sqrt{3}}{-3\left(\sqrt{3}\right)^{2}}+2=2\sqrt{3}$$

The square of \sqrt{3} is 3.

$$\frac{k\sqrt{3}}{-3\times 3}+2=2\sqrt{3}$$

Multiply -3 and 3 to get -9.

$$\frac{k\sqrt{3}}{-9}+2=2\sqrt{3}$$

Subtract 2 from both sides.

$$\frac{k\sqrt{3}}{-9}=2\sqrt{3}-2$$

Multiply both sides of the equation by -9.

$$k\sqrt{3}=-18\sqrt{3}+18$$

The equation is in standard form.

$$\sqrt{3}k=18-18\sqrt{3}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}k}{\sqrt{3}}=\frac{18-18\sqrt{3}}{\sqrt{3}}$$

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

$$k=\frac{18-18\sqrt{3}}{\sqrt{3}}$$

Divide -18\sqrt{3}+18 by \sqrt{3}.

$$k=6\sqrt{3}-18$$