The maximum bending moment occurs at a root of the equation:

you need to find the roots of this equation and classify it as a maxima or mininma or a point of inflection. In this case there is only one root and it should be obvious that it must correspond to a maximum. You should be able to do all this, if you have further problems please tell us exactly where they occur so we provide the specific help that you need to understand and solve this problem.

CB