Is there a method for determining the eigenvalues of a 3x3 matrix? The only examples my book does are already in upper triangular form, so det(1-tI) isn't exactly difficult (just multiply the diagonal). Any help on this? I've provided an example below!

$\displaystyle \left(\begin{array}{ccc}0&-2&-3\\-1&1&-1\\2&2&5\end{array}\right)$