Diagonalization & Matrix Powers · Challenge problem

Two coupled chemical concentrations evolve by $\mathbf x' = A\mathbf x$ with $A = \begin{pmatrix}-0.8 & -0.4\\0.6 & -2.2\end{pmatrix}$ and $\mathbf x(0) = \begin{pmatrix}7\\16\end{pmatrix}$. Diagonalize $A$ and find the first time $t>0$ at which the two concentrations are equal.