We have that
m + m^2 = 15/4
And
m * m^2 = a^3
m^3 = a^3
This implies that m = a
So
a + a^2 = 15/4
a^2 + a = 15/4 complete the square on a
a^2 + a + 1/4 = 15/4 + 1/4
(a + 1/2)^2 = 4 take both roots
a + 1/2 = ±√4
a + 1/2 = 2 or a + 1/2 = - 2
a = 3/2 or a = - 5 / 2