An object was thrown upward from the top of an 80ft tower. The height h of the object after t seconds is represented by the quadratic equation h=-16t^2 + 64t + 80. After how many seconds will the object hit the ground?

The problem gives you:
h=-16t^2+64t+80
where
h is height in feet
t is time in secs

If it hits the ground, h = 0 so 
set h=0 and solve for t:
h=-16t^2+64t+80
0=-16t^2+64t+80
0=-4t^2+16t+5
Solving using the quadratic equation yields:
t = {-0.29, 4.29}
We can throw out the negative solution leaving
t = 4.29 seconds