H(t)=-66t^2+8t+80

Solution for H(t)=-66t^2+8t+80 equation:

(H)=-66H^2+8H+80

We move all terms to the left:

(H)-(-66H^2+8H+80)=0

We get rid of parentheses

66H^2-8H+H-80=0

We add all the numbers together, and all the variables

66H^2-7H-80=0

a = 66; b = -7; c = -80;
Δ = b2-4ac
Δ = -72-4·66·(-80)
Δ = 21169
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{-(-7)-\sqrt{21169}}{2*66}=\frac{7-\sqrt{21169}}{132}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{21169}}{2*66}=\frac{7+\sqrt{21169}}{132}
$