Find all solutions of $7x^2 \equiv 1 \pmod {17}$ Find all solutions of $7x^2 \equiv 1 \pmod {17}$

I found out all the primitive root of $U_{17}$ to be : $\{3,5,6,7,10,12,14\}$.
To continue with the computation, I think i need to use the theorem which is $x^2 \equiv1\pmod{n}$. But Im not sure how to connect it with the question?
Thanks!!

$$7x^2 \equiv 1 \pmod{17} \implies x^2 \equiv 7^{-1} \pmod{17} \implies x^2 \equiv 5 \pmod{17}$$
When $(x,17) = 1$ from little-Fermat, we have
$$x^{16} \equiv 1 \pmod{17}$$
But we also need $x^2 \equiv 5 \pmod{17}$. This means $$x^{16} = {x^2}^8 \equiv 5^8 \pmod{17} \equiv (25)^4 \pmod{17} \equiv 8^4 \pmod{17} \equiv (64)^2 \pmod{17}$$
$$(64)^2 \pmod{17} \equiv 13^2 \pmod{17} \equiv 169 \pmod{17} \equiv -1 \pmod{17}$$
contradicting little-Fermat.
