Solve x^2=4a/sqrt{3}

$$x ^ { 2 } = \frac { 4 a } { \sqrt { 3 } }$$

Solve for a

$$a=\frac{\sqrt{3}x^{2}}{4}$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{4a}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$x^{2}=\frac{4a\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$x^{2}=\frac{4a\sqrt{3}}{3}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{4a\sqrt{3}}{3}=x^{2}$$

Multiply both sides of the equation by 3.

$$4a\sqrt{3}=3x^{2}$$

The equation is in standard form.

$$4\sqrt{3}a=3x^{2}$$

Divide both sides by 4\sqrt{3}.

$$\frac{4\sqrt{3}a}{4\sqrt{3}}=\frac{3x^{2}}{4\sqrt{3}}$$

Dividing by 4\sqrt{3} undoes the multiplication by 4\sqrt{3}.

$$a=\frac{3x^{2}}{4\sqrt{3}}$$

Divide 3x^{2} by 4\sqrt{3}.

$$a=\frac{\sqrt{3}x^{2}}{4}$$

Solve for x (complex solution)

$$x=-\frac{2\times 3^{\frac{3}{4}}\sqrt{a}}{3}$$

$$x=\frac{2\times 3^{\frac{3}{4}}\sqrt{a}}{3}$$

Solve for x

$$x=\frac{2\times 3^{\frac{3}{4}}\sqrt{a}}{3}$$

$$x=-\frac{2\times 3^{\frac{3}{4}}\sqrt{a}}{3}\text{, }a\geq 0$$