A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air h = - 162 + 24t + 16. How long will it take the gymnast to reach the ground?

That is when h=0

so assuming yo meant

h (t) = - 16t²+24t+16

solve for t such that h (t) = 0

because when height=0, the gymnast hits the ground

so

0=-16t²+24t+16

using math (imma complete the square

0=-16 (t²-3/2t) + 16

0=-16 (t²-3/2t+9/16-9/16) + 16

0=-16 ((t-3/4) ²-9/16) + 16

0=-16 (t-3/4) ²+9+16

0=-16 (t-3/4) ²+25

-25=-16 (t-3/4) ²

25/16 = (t-3/4) ²

sqrt both sides

+/-5/4=t-3/4

3/4+/-5/4=t

if we do plus (because minus would give us negative height)

8/4=t

2=t

it takes 2 seconds