How do I solve this

Question

A cannon ball is launched into the air with an upward velocity of 143 feet per second, from a 14-foot tall cannon. The height hh of the cannon ball after tt seconds can be found using the equation h=−16t2+143t+14h=-16t2+143t+14.

Approximately how long will it take for the cannon ball to be 276 feet high? Round answers to the nearest tenth if necessary.

 units: 

How long long will it take to hit the ground?

 units: 

Answer 1

-16t^2 + 143t + 14 = 276

-16t^2 + 143t - 262 = 0

t = 143/32 + or - (1/32)sqr(143^2 -4(16)(262))

t = (143 - 60.67)/32 = 82.33/32 = 2.6 seconds when the cannon ball reaches 276 feet

-16t^2 + 143 +14 = 0

t= 143/32 + (1/32)sqr(143^2 +4(16)(14))

t = (143 + 146.1)/32 = 289.1/32 = 9.0 seconds to reach the ground

it reaches max height when 32t = 143, t=143/32 = about 4.5 seconds.

to reach the ground is about twice the time to reach max height = 2(4.5) = 9.0 seconds