H=-4.9t^2+529.2t-50

Solution for H=-4.9t^2+529.2t-50 equation:

=-4.9H^2+529.2H-50

We move all terms to the left:

-(-4.9H^2+529.2H-50)=0

We get rid of parentheses

4.9H^2-529.2H+50=0

a = 4.9; b = -529.2; c = +50;
Δ = b2-4ac
Δ = -529.22-4·4.9·50
Δ = 279072.64
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{-(-529.2)-\sqrt{279072.64}}{2*4.9}=\frac{529.2-\sqrt{279072.64}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-529.2)+\sqrt{279072.64}}{2*4.9}=\frac{529.2+\sqrt{279072.64}}{9.8}
$