The charachteristic polynomial of two similar matrices are the same. Thus, if
has the charachteristic polynomial
then
by the
Cayley-Hamilton theorem. Of course, this theorem is very advanced and you probably never seen it before. Therefore, there is a weaker version for this theorem which states that a diagnolizable matrix satisfies its charachteristic polynomial. Since
is a symettric matrix it means it is diagnolizable and the rest follows.
Thus, you need to find
which solve this polynomial equation.