The equation y = -6t^2 + 51t describes the height (in feet) of a projectile launched from the surface of Mars at 51 feet per second. In how many seconds will the projectile first reach 108 feet in height?

We need to solve this

108 = - 6t^2 + 51t rearrange as

6t^2 - 51t + 108 = 0 divide through by 3

2t^2 - 17t + 36 = 0 factor

(2t - 9) (t - 4) = 0

Set each factor to 0 and solve

2t -9 = 0 t - 4 =0

2t = 9 t = 4 sec

t = 9/2 sec = 4.5 sec

So...4 sec