H=-16t^2-220t-45

Solution for H=-16t^2-220t-45 equation:

=-16H^2-220H-45

We move all terms to the left:

-(-16H^2-220H-45)=0

We get rid of parentheses

16H^2+220H+45=0

a = 16; b = 220; c = +45;
Δ = b2-4ac
Δ = 2202-4·16·45
Δ = 45520
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:

$\sqrt{\Delta}=\sqrt{45520}=\sqrt{16*2845}=\sqrt{16}*\sqrt{2845}=4\sqrt{2845}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-4\sqrt{2845}}{2*16}=\frac{-220-4\sqrt{2845}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+4\sqrt{2845}}{2*16}=\frac{-220+4\sqrt{2845}}{32}
$