If you have the Symbolic Math Toolbox, use the solve function:
syms a hs hp Mt
It = Mt * (a^2/6 + ((a + hs)/2 + hp)^2);
a_sol = solve(It, a)
a_sol_simp = simplify(a_sol, 'Steps',10)
a_sol =
- (6*hp)/5 - (3*hs)/5 - (6^(1/2)*hp*2i)/5 - (6^(1/2)*hs*1i)/5
- (6*hp)/5 - (3*hs)/5 + (6^(1/2)*hp*2i)/5 + (6^(1/2)*hs*1i)/5
a_sol_simp =
-((3 + 6^(1/2)*1i)*(2*hp + hs))/5
((2*hp + hs)*(6^(1/2) + 3i)*1i)/5
