Question

Help me with this question please thank you 

A ball is thrown downward from a window from a tall building. Its position at time t in seconds is s = 16t^2 + 32t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 161 feet.

Answer 1

if I understood correctly:
s = 16t^2 + 32t, s=161
16t^2 + 32t=161
16t^2 + 32t-161=0
t=(-32+8√177)/32=-1+√177/4≈2,326≈2,3

Answer 2

`s=16t^2+32t;\ s=161\\\\16t^2+32t=161\\\\16t^2+32t-161=0\\\\a=16;\ b=32;\ c=-161\\\\\Delta=b^2-4ac\to\Delta=32^2-4\cdot16\cdot(-161)=1024+10304=11328\\\\x_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\\\\√(11328)=√(64\cdot177)=8√(177)\approx106.4\\\\x_1=(-32-106.4)/(2\cdot16)< 0;\ x_2=(-32+106.4)/(2\cdot16)=(74.4)/(32)=2.325\approx2.3\ (ft)`