Yolanda throws a sphere up in the air from the top of a building. Help!!!!

After  t  seconds, the height of the sphere above the ground is  h  feet, where

 

h  =  -16t² + 30t + 78

 

After how many seconds does the sphere hit the ground?

 

When the sphere is on the ground, its height is zero. We want to know the time when the height of the sphere is zero. That is, we want to know  t  when  h = 0 . We want to know the value of  t  that makes this equation true:

 

0  =  -16t² + 30t + 78

                                          To solve for  t , let's first divide both sides of the equation by  2 .

0  =  -8t² + 15t + 39

                                          Now let's solve this quadratic equation using the quadratic formula.

t  =  \({-15 \pm \sqrt{15^2-4(-8)(39)} \over 2(-8)}\)

 

t   =   \({-15 \pm \sqrt{225+1248} \over -16}\)

 

t   =   \({-15 \pm \sqrt{1473} \over -16}\)

 

t   =   \({-15 + \sqrt{1473} \over -16}\)          or          t  =  \({-15 - \sqrt{1473} \over -16}\)

 

t  ≈  -1.461                    or          t  ≈  3.336

 

Since  t  is a measure of time, it should be the positive option.

 

So...the sphere hits the ground after about  3.336  seconds.

Just confirming before answer, is this what the question lloks like 

Yolanda throws a sphere up in the air from the top of a building. After t² seconds, the height of the sphere above the ground is h² feet, where h=−16t²+30t+78. After how many seconds does the sphere hit the ground?