H=-16t^2-55t+10

Solution for H=-16t^2-55t+10 equation:

=-16H^2-55H+10

We move all terms to the left:

-(-16H^2-55H+10)=0

We get rid of parentheses

16H^2+55H-10=0

a = 16; b = 55; c = -10;
Δ = b2-4ac
Δ = 552-4·16·(-10)
Δ = 3665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-\sqrt{3665}}{2*16}=\frac{-55-\sqrt{3665}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3665}}{2*16}=\frac{-55+\sqrt{3665}}{32}
$