The trajectory of a ball thrown in the air is given by h(t)= −4t2+16t−10 , where h is the height in metres and t is the time in seconds. How long is the ball above 2 meters?

Answer 1

2 = −4 t^2 + 16 t − 10

subtracting 2 ... 0 = −4 t^2 + 16 t − 8

dividing by 4 ... 0 = − t^2 + 4 t − 2

find the two roots (quadratic formula)

the difference in the roots is the time above 2 m

Answer 2

I think you meant
0 = −4 t^2 + 16 t − 12
now solve that.