H (t) = -16t^2+24t+40.0

t = - 1 or 5/2

Step-by-step explanation:

To find t; we equate H (t) = 0

-16t^2+24t+40.0 = 0

dividing through by 8 we have;

-16t^2 / 8 + 24t/8+40.0/8=0

-2t^2 + 3t + 5=0

-2t^2 + 5t - 2t + 5=0

By factorisation;

t (-2t + 5) + 1 (-2t + 5) = 0

This means;

(t + 1) (-2t + 5) = 0

t + 1 = 0 or - 2t + 5 = 0;

t = - 1; - 2t = - 5

2t = 5

t = 5/2;

Hence t = - 1 or 5/2