well the way you are meant to do it:
you want to sovle a^3 + 3a - 140 = 0
after a bit of trying you discover that a=5 is a solution.
then you factorize it:
(a-5)(a^2 + 5a + 28) = 0
and since a^2 + 5a + 28 = 0 has no real valued solutions, a = 5 is the only real solution.
the general way:
let a...