H(t)=80t+5t2

Solution for H(t)=80t+5t2 equation:

(H)=80H+5H^2

We move all terms to the left:

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

We get rid of parentheses

-5H^2-80H+H=0

We add all the numbers together, and all the variables

-5H^2-79H=0

a = -5; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·(-5)·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*-5}=\frac{0}{-10}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*-5}=\frac{158}{-10}
=-15+4/5
$