H=-12.6+19.6t+4.9t2

Solution for H=-12.6+19.6t+4.9t2 equation:

=-12.6+19.6H+4.9H^2

We move all terms to the left:

-(-12.6+19.6H+4.9H^2)=0

We get rid of parentheses

-4.9H^2-19.6H+12.6=0

a = -4.9; b = -19.6; c = +12.6;
Δ = b2-4ac
Δ = -19.62-4·(-4.9)·12.6
Δ = 631.12
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{-(-19.6)-\sqrt{631.12}}{2*-4.9}=\frac{19.6-\sqrt{631.12}}{-9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19.6)+\sqrt{631.12}}{2*-4.9}=\frac{19.6+\sqrt{631.12}}{-9.8}
$