H(t)=-4.9t^2+25t+25

Solution for H(t)=-4.9t^2+25t+25 equation:

(H)=-4.9H^2+25H+25

We move all terms to the left:

(H)-(-4.9H^2+25H+25)=0

We get rid of parentheses

4.9H^2-25H+H-25=0

We add all the numbers together, and all the variables

4.9H^2-24H-25=0

a = 4.9; b = -24; c = -25;
Δ = b2-4ac
Δ = -242-4·4.9·(-25)
Δ = 1066
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)-\sqrt{1066}}{2*4.9}=\frac{24-\sqrt{1066}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+\sqrt{1066}}{2*4.9}=\frac{24+\sqrt{1066}}{9.8}
$