H=-4.9t^2+24.5t+6

Solution for H=-4.9t^2+24.5t+6 equation:

=-4.9H^2+24.5H+6

We move all terms to the left:

-(-4.9H^2+24.5H+6)=0

We get rid of parentheses

4.9H^2-24.5H-6=0

a = 4.9; b = -24.5; c = -6;
Δ = b2-4ac
Δ = -24.52-4·4.9·(-6)
Δ = 717.85
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{-(-24.5)-\sqrt{717.85}}{2*4.9}=\frac{24.5-\sqrt{717.85}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24.5)+\sqrt{717.85}}{2*4.9}=\frac{24.5+\sqrt{717.85}}{9.8}
$