Finding eigenvalues and eigenvectors of a real matrix

Okay, so the matrix is...

$\displaystyle \left(\begin{array}{cc}6 & 5 \\ -5 & 0\end{array}\right)$

I solved $\displaystyle det(A-\lambda I)=0$ to find $\displaystyle \lambda$ (which is the method I was taught), and I ended up with $\displaystyle \lambda=3\pm4i$, but now I'm a bit stuck. I've written down...

$\displaystyle \left(\begin{array}{cc}6 & 5 \\ -5 & 0\end{array}\right)\left(\begin{array}{c}x \\ y\end{array}\right)=(3\pm4i)\left(\begin{array}{c} x \\ y\end{array}\right)$

... but I can't seem to manipulate it to get the eigenvectors.