Systems of Differential Equations · Hard problem

A system $\mathbf x'=A\mathbf x$ with $A=\begin{pmatrix}-5/2&3/2\\3/2&-5/2\end{pmatrix}$ starts at $(3,-1)$. Its solution is a combination of two decaying exponential terms, one for each eigenvalue of $A$. Find the time at which these two exponential terms are equal in size.