Eigenvalues from trace and determinant

Let $\alpha$, $\beta$ and $\gamma$ be the eigenvalues of $M=\begin{pmatrix}0&1&0\\1&3&3\\-1&2&2\end{pmatrix}$. If $\gamma=1$ and $\alpha>\beta$, then the value of $2\alpha+3\beta$ is __________.