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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16H^2-55H-25=0

a = 16; b = -55; c = -25;
Δ = b2-4ac
Δ = -552-4·16·(-25)
Δ = 4625
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:

$\sqrt{\Delta}=\sqrt{4625}=\sqrt{25*185}=\sqrt{25}*\sqrt{185}=5\sqrt{185}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{185}}{2*16}=\frac{55-5\sqrt{185}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{185}}{2*16}=\frac{55+5\sqrt{185}}{32}
$