H(t)=-9t^2+20t+20

Solution for H(t)=-9t^2+20t+20 equation:

(H)=-9H^2+20H+20

We move all terms to the left:

(H)-(-9H^2+20H+20)=0

We get rid of parentheses

9H^2-20H+H-20=0

We add all the numbers together, and all the variables

9H^2-19H-20=0

a = 9; b = -19; c = -20;
Δ = b2-4ac
Δ = -192-4·9·(-20)
Δ = 1081
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{-(-19)-\sqrt{1081}}{2*9}=\frac{19-\sqrt{1081}}{18}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1081}}{2*9}=\frac{19+\sqrt{1081}}{18}
$