Assuming the matrix is
[tex]\mathbf A=\begin{bmatrix}-8&3\\-3&10\end{bmatrix}[/tex]
we have characteristic polynomial given by the equation
[tex]\det(\mathbf A-\lambda \mathbf I)=0\iff\begin{vmatrix}-8-\lambda&3\\-3&10-\lambda\end{vmatrix}=0[/tex]
[tex](-8-\lambda)(10-\lambda)-(-9)=0[/tex]
[tex]\lambda^2-2\lambda-71=0[/tex]
