Taking the fixed support to be the moment center, the moment diagram by parts is shown to the right.

$EI \, t_{A/B} = (Area_{AB})\, \bar{X}_A = 0$

$ML(\frac{1}{2}L) – \frac{1}{2}L(RL)(\frac{2}{3}L) = 0$

$\frac{1}{2}ML^2 – \frac{1}{3}RL^3 = 0$

$R = \dfrac{3M}{2L}$ *answer*