H(t)=-16t2+210t

Solution for H(t)=-16t2+210t equation:

(H)=-16H^2+210H

We move all terms to the left:

(H)-(-16H^2+210H)=0

We get rid of parentheses

16H^2-210H+H=0

We add all the numbers together, and all the variables

16H^2-209H=0

a = 16; b = -209; c = 0;
Δ = b2-4ac
Δ = -2092-4·16·0
Δ = 43681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43681}=209$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-209)-209}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-209)+209}{2*16}=\frac{418}{32}
=13+1/16
$