Solving a word problem using a quadratic equation with irration

Question

A model rocket is launched with an initial upward velocity of 138/fts. The rocket's height h (in feet) after t seconds is given by the following.=h−138t16t2 Find all values of t for which the rocket's height is 78 feet.

Answer 1

h(t) = -16t^2 + 138t -78 =0

16t^2 -138t + 78 = 0

t = 138/32 + or - (1/32)sqr(138^2 -64(78))

= 4.3125 + or - (1/32)sqr(19044-4992)

= 4.3 + or 3.7 = 0.6 or 8 seconds

h' = -32t+138 = 0

t = 138/32 = 4.3 at maximum height

-16(4.3)^2 + 138(4.3) -78 = -295.8 + 593.4 -78 = 219.6 = max height in 4.3 seconds

78 feet in 0.6 and 8 seconds a the rocket goes up and down,