I'm trying to find the Eigenvalues of the following $2\times 2$ matrix :
$$
\begin{bmatrix}-2 & -7\\
1 & 2\end{bmatrix}
$$

I've been getting mixed results: by hand I've tried calculating the eigenvalue and I ended up with $-\sqrt{11}$ and $\sqrt{11}$. But when I used maple to help me calculate the eigenvalues it gives me the following non-real numbers:
$i\sqrt{3}$
$-i\sqrt{3}$

From what I've checked the answer Maple is giving me is correct and the one I keep getting by hand is incorrect. I would like some help understanding how I can get the same result manually if possible. Thanks for your time.