H(t)=16t^2+1024t

Solution for H(t)=16t^2+1024t equation:

(H)=16H^2+1024H

We move all terms to the left:

(H)-(16H^2+1024H)=0

We get rid of parentheses

-16H^2+H-1024H=0

We add all the numbers together, and all the variables

-16H^2-1023H=0

a = -16; b = -1023; c = 0;
Δ = b2-4ac
Δ = -10232-4·(-16)·0
Δ = 1046529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1046529}=1023$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1023)-1023}{2*-16}=\frac{0}{-32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1023)+1023}{2*-16}=\frac{2046}{-32}
=-63+15/16
$