H=-14t^2+476t

Solution for H=-14t^2+476t equation:

=-14H^2+476H

We move all terms to the left:

-(-14H^2+476H)=0

We get rid of parentheses

14H^2-476H=0

a = 14; b = -476; c = 0;
Δ = b2-4ac
Δ = -4762-4·14·0
Δ = 226576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{226576}=476$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-476)-476}{2*14}=\frac{0}{28}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-476)+476}{2*14}=\frac{952}{28}
=34
$