H(t)=16t^2+80t+5

Solution for H(t)=16t^2+80t+5 equation:

(H)=16H^2+80H+5

We move all terms to the left:

(H)-(16H^2+80H+5)=0

We get rid of parentheses

-16H^2+H-80H-5=0

We add all the numbers together, and all the variables

-16H^2-79H-5=0

a = -16; b = -79; c = -5;
Δ = b2-4ac
Δ = -792-4·(-16)·(-5)
Δ = 5921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-\sqrt{5921}}{2*-16}=\frac{79-\sqrt{5921}}{-32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{5921}}{2*-16}=\frac{79+\sqrt{5921}}{-32}
$