H=20t-5t^2+60

Solution for H=20t-5t^2+60 equation:

=20H-5H^2+60

We move all terms to the left:

-(20H-5H^2+60)=0

We get rid of parentheses

5H^2-20H-60=0

a = 5; b = -20; c = -60;
Δ = b2-4ac
Δ = -202-4·5·(-60)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-40}{2*5}=\frac{-20}{10}
=-2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+40}{2*5}=\frac{60}{10}
=6
$