H=-16t^2+45t+50

Solution for H=-16t^2+45t+50 equation:

=-16H^2+45H+50

We move all terms to the left:

-(-16H^2+45H+50)=0

We get rid of parentheses

16H^2-45H-50=0

a = 16; b = -45; c = -50;
Δ = b2-4ac
Δ = -452-4·16·(-50)
Δ = 5225
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:

$\sqrt{\Delta}=\sqrt{5225}=\sqrt{25*209}=\sqrt{25}*\sqrt{209}=5\sqrt{209}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5\sqrt{209}}{2*16}=\frac{45-5\sqrt{209}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5\sqrt{209}}{2*16}=\frac{45+5\sqrt{209}}{32}
$