$\delta_1 = \dfrac{RL^3}{3EI}$

$\delta_2 = \dfrac{w_oL^4}{8EI} - \dfrac{RL^3}{3EI}$

$\delta_1 = \delta_2$

$\dfrac{RL^3}{3EI} = \dfrac{w_oL^4}{8EI} - \dfrac{RL^3}{3EI}$

$\dfrac{2RL^3}{3EI} = \dfrac{w_oL^4}{8EI}$

$R = \dfrac{3w_oL}{16}$

$M_A = -RL$

$M_A = -\dfrac{3w_oL^2}{16}$ *answer*

$M_B = RL - w_oL(\frac{1}{2}L)$

$M_B = \dfrac{3w_oL^2}{16} - \dfrac{w_oL^2}{2}$

$M_B = -\dfrac{5w_oL^2}{16}$ *answer*