Please help on algebra

Question

A baseball player hit a ball with an upward velocity of 48 ft/s. Its height in feet after t seconds is given by the function f(x)=−16 t 2 +48t+6. f(x)=-16t^2+48t+6. What is the maximum height the ball reaches? How long will it take the baseball to reach the maximum height? How long will it take for the ball to hit the ground?

Answer 1

-16t^2 + 48t + 6 = 0

8t^2 - 24t - 3 = 0 <--- divide by -2

t = [24 +or- sqrt ( (-24)^2 - 4(8)(-3))] / 16

= [ 24 +or- sqrt( 576 + 72]/16

= [ 24 +or- sqrt( 648) ] /16

= [ 24 +or- sqrt ( 2*2*2*3 *3*3*3)]/16

= [ 24 +or- 2*3*3*sqrt(2)]/16

= [24 +or- 18*sqrt(2)]/16

= [ 12 +or- 9*Sqrt(2)]/ 8

The negative branch results in negative times

t=3.090990257669732 <--- how long it takes the ball to hit the ground

max occurs at t = -b/2a = 3/2 = 1.5 <--- time to max height

f(1.5) = 42 <--- max height