Solving the equation $\frac{gy}{x} + \frac{2y^2}{x} = \frac{gy}{y^2} + \frac{2x}{y^2}$ for $x$ or $y$ One day, while making and doing math problems, I came across this equation:

$$\frac{gy}{x} + \frac{2y^2}{x} = \frac{gy}{y^2} + \frac{2x}{y^2}$$

After some simple steps, I found $g$, but I couldn't find $x$ or $y$.
Here's a picture, since I'm not good with MathJax.


Multiplying by $$x\ne 0$$ we get
$$gy+2y^2=\frac{gx}{y}+\frac{2x^2}{y^2}$$
Now you can multiply by $$y^2$$
We get
$$gy^3+2y^4=gxy+2x^2$$
