H(t)=80-5*t^2

Solution for H(t)=80-5*t^2 equation:

(H)=80-5H^2

We move all terms to the left:

(H)-(80-5H^2)=0

We get rid of parentheses

5H^2+H-80=0

a = 5; b = 1; c = -80;
Δ = b2-4ac
Δ = 12-4·5·(-80)
Δ = 1601
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{-(1)-\sqrt{1601}}{2*5}=\frac{-1-\sqrt{1601}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1601}}{2*5}=\frac{-1+\sqrt{1601}}{10}
$