I think this is what the equation is:
H(t) = -4.9t^2 + 40t
We want to know what t is when h(t) = 75
So plug in 75 for h(t) and solve for t.
75 = -4.9t^2 + 40t
Subtract 75 from both sides.
0 = -4.9t2 + 40t - 75
Now we can use the quadratic formula to solve for t.
\(t = {-40 \pm \sqrt{40^2-4(-4.9)(-75)} \over 2(-4.9)}\\~\\t={-40 \pm \sqrt{130} \over -9.8}\\~\\ t=\frac{-40+\sqrt{130}}{-9.8}\qquad\text{or}\qquad t=\frac{-40-\sqrt{130}}{-9.8}\)
t ≈ 5.245 seconds or t ≈ 2.918 seconds
