H=-16t^2+55t+50

Solution for H=-16t^2+55t+50 equation:

=-16H^2+55H+50

We move all terms to the left:

-(-16H^2+55H+50)=0

We get rid of parentheses

16H^2-55H-50=0

a = 16; b = -55; c = -50;
Δ = b2-4ac
Δ = -552-4·16·(-50)
Δ = 6225
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:

$\sqrt{\Delta}=\sqrt{6225}=\sqrt{25*249}=\sqrt{25}*\sqrt{249}=5\sqrt{249}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{249}}{2*16}=\frac{55-5\sqrt{249}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{249}}{2*16}=\frac{55+5\sqrt{249}}{32}
$