H(t)=-6t^2-8t+80

Solution for H(t)=-6t^2-8t+80 equation:

(H)=-6H^2-8H+80

We move all terms to the left:

(H)-(-6H^2-8H+80)=0

We get rid of parentheses

6H^2+8H+H-80=0

We add all the numbers together, and all the variables

6H^2+9H-80=0

a = 6; b = 9; c = -80;
Δ = b2-4ac
Δ = 92-4·6·(-80)
Δ = 2001
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{-(9)-\sqrt{2001}}{2*6}=\frac{-9-\sqrt{2001}}{12}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{2001}}{2*6}=\frac{-9+\sqrt{2001}}{12}
$