H(t)=58t-0.82t^2

Solution for H(t)=58t-0.82t^2 equation:

(H)=58H-0.82H^2

We move all terms to the left:

(H)-(58H-0.82H^2)=0

We get rid of parentheses

0.82H^2-58H+H=0

We add all the numbers together, and all the variables

0.82H^2-57H=0

a = 0.82; b = -57; c = 0;
Δ = b2-4ac
Δ = -572-4·0.82·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-57}{2*0.82}=\frac{0}{1.64}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+57}{2*0.82}=\frac{114}{1.64}
=69+0.84/1.64
$