All are easy. There is no way to say thatnone way is easier than the other. Well the answer lies in every individual, it depends on which method they are comfortable with. Anyway there are more method to solve quadratic than the listed ones.
Recall that the characteristic polynomial of a 2x2 matrix
is
but
and
, so the characteristic polynomial for
is
We're given that the trace is 15 and determinant is 50, so the characteristic polynomial for the matrix in question is
and the eigenvalues are those
for which the characteristic polynomial evaluates to 0.
I’m very confused what are you trying to do here ?