Explanation:
it is still precisely the same method and formula just with different numbers.
y = -16x² + 212x + 139
we assume, the ground is at 0 ft.
so, we need to solve
0 = -16x² + 212x + 139
the general solution for such quadratic equations is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = -16
b = 212
c = 139
x = (-212 ± sqrt(212² - 4×-16×139))/(2×-16) =
= (-212 ± sqrt(44944 + 8896))/-32 =
= (-212 ± sqrt(53840))/-32
x1 = (-212 + 232.0344802...)/-32 = -0.626077506... s
x2 = (-212 - 232.0344802...)/-32 = 13.87607751... s
again, the negative solution for time did not make any sense, so, x2 is our solution.
the rocket will hit the ground after about 13.88 seconds.