H=-16t^2+100t+25

Solution for H=-16t^2+100t+25 equation:

=-16H^2+100H+25

We move all terms to the left:

-(-16H^2+100H+25)=0

We get rid of parentheses

16H^2-100H-25=0

a = 16; b = -100; c = -25;
Δ = b2-4ac
Δ = -1002-4·16·(-25)
Δ = 11600
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:

$\sqrt{\Delta}=\sqrt{11600}=\sqrt{400*29}=\sqrt{400}*\sqrt{29}=20\sqrt{29}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{29}}{2*16}=\frac{100-20\sqrt{29}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{29}}{2*16}=\frac{100+20\sqrt{29}}{32}
$