H(t)=-16t2+80t+21

Solution for H(t)=-16t2+80t+21 equation:

(H)=-16H^2+80H+21

We move all terms to the left:

(H)-(-16H^2+80H+21)=0

We get rid of parentheses

16H^2-80H+H-21=0

We add all the numbers together, and all the variables

16H^2-79H-21=0

a = 16; b = -79; c = -21;
Δ = b2-4ac
Δ = -792-4·16·(-21)
Δ = 7585
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{7585}}{2*16}=\frac{79-\sqrt{7585}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{7585}}{2*16}=\frac{79+\sqrt{7585}}{32}
$