Question 27374
This is a basic quadratic equation exercise. We want to find the t at which the rocket hits the ground. The fact that it hits the ground implies that the its height is now zero. So we must solve the equation:

{{{-16t^2+80t+96 = 0}}}

We use the standard procedure:

*[invoke solve_quadratic_equation -16, 80, 96]

The two solutions are -1 and 6, but since time cannot be negative, the relevant solution is 6. The rocket hits the ground 6 seconds after it's launched.