H=-16t^2+220t+31

Solution for H=-16t^2+220t+31 equation:

=-16H^2+220H+31

We move all terms to the left:

-(-16H^2+220H+31)=0

We get rid of parentheses

16H^2-220H-31=0

a = 16; b = -220; c = -31;
Δ = b2-4ac
Δ = -2202-4·16·(-31)
Δ = 50384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{50384}=\sqrt{16*3149}=\sqrt{16}*\sqrt{3149}=4\sqrt{3149}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-4\sqrt{3149}}{2*16}=\frac{220-4\sqrt{3149}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+4\sqrt{3149}}{2*16}=\frac{220+4\sqrt{3149}}{32}
$