Solve fx^2+3y^2=4

$$f x ^ { 2 } + 3 y ^ { 2 } = 4$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{3y^{2}-4}{x^{2}}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&\left(y=\frac{2\sqrt{3}}{3}\text{ or }y=-\frac{2\sqrt{3}}{3}\right)\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3y^{2} from both sides.

$$fx^{2}=4-3y^{2}$$

The equation is in standard form.

$$x^{2}f=4-3y^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}f}{x^{2}}=\frac{4-3y^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$f=\frac{4-3y^{2}}{x^{2}}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{3y^{2}-4}{x^{2}}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ and }|y|=\frac{2\sqrt{3}}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3y^{2} from both sides.

$$fx^{2}=4-3y^{2}$$

The equation is in standard form.

$$x^{2}f=4-3y^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}f}{x^{2}}=\frac{4-3y^{2}}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$f=\frac{4-3y^{2}}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-if^{-\frac{1}{2}}\sqrt{3y^{2}-4}\text{; }x=if^{-\frac{1}{2}}\sqrt{3y^{2}-4}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&\left(y=\frac{2\sqrt{3}}{3}\text{ or }y=-\frac{2\sqrt{3}}{3}\right)\text{ and }f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{-\frac{3y^{2}-4}{f}}\text{; }x=-\sqrt{-\frac{3y^{2}-4}{f}}\text{, }&\left(f>0\text{ or }|y|\geq \frac{2\sqrt{3}}{3}\right)\text{ and }f\neq 0\text{ and }\left(f<0\text{ or }|y|\leq \frac{2\sqrt{3}}{3}\right)\\x\in \mathrm{R}\text{, }&f=0\text{ and }|y|=\frac{2\sqrt{3}}{3}\end{matrix}\right.$$