H(t)=-4.9t^2-30t+200

Solution for H(t)=-4.9t^2-30t+200 equation:

(H)=-4.9H^2-30H+200

We move all terms to the left:

(H)-(-4.9H^2-30H+200)=0

We get rid of parentheses

4.9H^2+30H+H-200=0

We add all the numbers together, and all the variables

4.9H^2+31H-200=0

a = 4.9; b = 31; c = -200;
Δ = b2-4ac
Δ = 312-4·4.9·(-200)
Δ = 4881
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{-(31)-\sqrt{4881}}{2*4.9}=\frac{-31-\sqrt{4881}}{9.8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{4881}}{2*4.9}=\frac{-31+\sqrt{4881}}{9.8}
$