H=25t-9.8t^2

Solution for H=25t-9.8t^2 equation:

=25H-9.8H^2

We move all terms to the left:

-(25H-9.8H^2)=0

We get rid of parentheses

9.8H^2-25H=0

a = 9.8; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·9.8·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*9.8}=\frac{0}{19.6}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*9.8}=\frac{50}{19.6}
=2+6/10.888888888889
$