H(x)=-16t^3+100t=72

Answer 1

or, just do the math.
-16t^3+100t=72
16t^3 - 100t + 72 = 0
4t^3 - 25t + 18 = 0
A little synthetic division yields
(t-2)(4t^2 + 8t - 9)
Now apply the quadratic formula and you get the roots are
t = 2, (-2±√13)/2