Is there any way to know what integer values of $n$ will satisfy
$an^2 + bn + c = x^2$?
In other words, what values of $n$ will make $an^2 + bn + c$ a perfect square, with $a, b, c$ given?
For example, for
$ a = 100, b = 8784, c = 3491 $
we have $n= 127$, then the RHS will be $x^2=1653^2 = 2732409$.
While this example could be done easily with Excel, how can I solve the problem for general $(a,b,c)$?