Could you explain to me how to solve "more sophisticated" matrix equations such as this one?

Prove that 2x^2 + x = \begin{bmatrix} -1&5&3\\-2&1&2\\0&-4&-3\end{bmatrix} has no solutions in M(3,3;R), where M(3,3;R) is the space of all matrices 3x3 with real entries.