We looked at linear congruences and now we want to look at congruences of the form
$$
\begin{align*}
ax^2 + bx + c \equiv 0 \pmod{p}
\end{align*}
$$
If we complete the square then we get
$$
\begin{align*}
a(x + b/2)^2 \equiv \frac{b^2 - 4ac}{4a} \pmod{p}
\end{align*}
$$