H(t)=85t-16t^2

Solution for H(t)=85t-16t^2 equation:

(H)=85H-16H^2

We move all terms to the left:

(H)-(85H-16H^2)=0

We get rid of parentheses

16H^2-85H+H=0

We add all the numbers together, and all the variables

16H^2-84H=0

a = 16; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·16·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*16}=\frac{168}{32}
=5+1/4
$