H=-16t^2+56t+25

Solution for H=-16t^2+56t+25 equation:

=-16H^2+56H+25

We move all terms to the left:

-(-16H^2+56H+25)=0

We get rid of parentheses

16H^2-56H-25=0

a = 16; b = -56; c = -25;
Δ = b2-4ac
Δ = -562-4·16·(-25)
Δ = 4736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4736}=\sqrt{64*74}=\sqrt{64}*\sqrt{74}=8\sqrt{74}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{74}}{2*16}=\frac{56-8\sqrt{74}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{74}}{2*16}=\frac{56+8\sqrt{74}}{32}
$