quadratics math plz help

Question

Devyn decides to try platform diving. She is using a 24-foot platform and would like to generate an initial velocity of 8 feet per second, which would be approximated by the function , h(t) = -16t^2 + 8t + 24. (t is the time in seconds). determine how long Devyn is in the air before she reaches the water.

Answer 1

1.5 seconds -- the diver enters the water at h(t) = 0, hence 0 = -16t^2 +8t +24 which reduces to 2t^2 -t -3 = 0

and that equation factors into (2t-3)(t+1) = 0 -- the solution is t =1.5, -1 and time cannot be negative, therefore the answer is 1.5