H(t)=-16t2+80t+384

Solution for H(t)=-16t2+80t+384 equation:

(H)=-16H^2+80H+384

We move all terms to the left:

(H)-(-16H^2+80H+384)=0

We get rid of parentheses

16H^2-80H+H-384=0

We add all the numbers together, and all the variables

16H^2-79H-384=0

a = 16; b = -79; c = -384;
Δ = b2-4ac
Δ = -792-4·16·(-384)
Δ = 30817
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{30817}}{2*16}=\frac{79-\sqrt{30817}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{30817}}{2*16}=\frac{79+\sqrt{30817}}{32}
$