Solve frac{(2x)(frac{sqrt{3}}{2}x)(y)}{2}=2007

$$\frac { ( 2 x ) ( \frac { \sqrt { 3 } } { 2 } x ) ( y ) } { 2 } = 2007$$

Solve for y

$$y=\frac{1338\sqrt{3}}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides by 2.

$$2x\times \frac{\sqrt{3}}{2}xy=2007\times 2$$

Cancel out 2 on both sides.

$$x\times \frac{\sqrt{3}}{2}xy=2007$$

Multiply both sides of the equation by 2.

$$x\sqrt{3}xy=4014$$

Multiply x and x to get x^{2}.

$$x^{2}\sqrt{3}y=4014$$

The equation is in standard form.

$$\sqrt{3}x^{2}y=4014$$

Divide both sides by x^{2}\sqrt{3}.

$$\frac{\sqrt{3}x^{2}y}{\sqrt{3}x^{2}}=\frac{4014}{\sqrt{3}x^{2}}$$

Dividing by x^{2}\sqrt{3} undoes the multiplication by x^{2}\sqrt{3}.

$$y=\frac{4014}{\sqrt{3}x^{2}}$$

Divide 4014 by x^{2}\sqrt{3}.

$$y=\frac{1338\sqrt{3}}{x^{2}}$$

Solve for x (complex solution)

$$x=-\sqrt[4]{5370732}y^{-\frac{1}{2}}$$

$$x=\sqrt[4]{5370732}y^{-\frac{1}{2}}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt[4]{5370732}}{\sqrt{y}}$$

$$x=-\frac{\sqrt[4]{5370732}}{\sqrt{y}}\text{, }y>0$$