Showing that relation $f$ is a function

Question

How can I determine if the relation $f$ on $\mathbb{R}$ given by $xfy\Leftrightarrow (y(2x-3)-3x=y(x^2-2x)-5x^2)$ is a function?

I've tried plotting the function as a quadratic function, and doing the vertical line test (but without success)

Answer 1

Unless you made a mistake, the condition is $$ y=\frac{3x-5x^2}{2x-3-x^2+2x}=\frac{3x-5x^2}{-x^2+4x-3}. $$ Of course as long as $-x^2+4x-3 \neq 0$.