H=39.2t-4.9t2

Solution for H=39.2t-4.9t2 equation:

=39.2H-4.9H^2

We move all terms to the left:

-(39.2H-4.9H^2)=0

We get rid of parentheses

4.9H^2-39.2H=0

a = 4.9; b = -39.2; c = 0;
Δ = b2-4ac
Δ = -39.22-4·4.9·0
Δ = 1536.64
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{-(-39.2)-\sqrt{1536.64}}{2*4.9}=\frac{39.2-\sqrt{1536.64}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39.2)+\sqrt{1536.64}}{2*4.9}=\frac{39.2+\sqrt{1536.64}}{9.8}
$