Math question related to functional equations

Question

The function $f$ satisfies $f(x) + f(2x + y) + 5xy = f(3x - y) + 2x^2 + 1$for all real numbers $x$, $y$. Determine the value of $f(10)$.

Answer 1

meanwhile, there really is such a function, $$ f(w) = -\frac{1}{2} w^2 + 1 $$ works

Answer 2

Let $x=10, y=5$. Then the condition becomes $$f(10)+f(25)+250=f(25)+201$$ Which implies that $f(10)=-49$.