H(t)=-16t^2+75t+80

Solution for H(t)=-16t^2+75t+80 equation:

(H)=-16H^2+75H+80

We move all terms to the left:

(H)-(-16H^2+75H+80)=0

We get rid of parentheses

16H^2-75H+H-80=0

We add all the numbers together, and all the variables

16H^2-74H-80=0

a = 16; b = -74; c = -80;
Δ = b2-4ac
Δ = -742-4·16·(-80)
Δ = 10596
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:

$\sqrt{\Delta}=\sqrt{10596}=\sqrt{4*2649}=\sqrt{4}*\sqrt{2649}=2\sqrt{2649}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{2649}}{2*16}=\frac{74-2\sqrt{2649}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{2649}}{2*16}=\frac{74+2\sqrt{2649}}{32}
$