H(t)=-16t^2+10t+25

Solution for H(t)=-16t^2+10t+25 equation:

(H)=-16H^2+10H+25

We move all terms to the left:

(H)-(-16H^2+10H+25)=0

We get rid of parentheses

16H^2-10H+H-25=0

We add all the numbers together, and all the variables

16H^2-9H-25=0

a = 16; b = -9; c = -25;
Δ = b2-4ac
Δ = -92-4·16·(-25)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-41}{2*16}=\frac{-32}{32}
=-1
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+41}{2*16}=\frac{50}{32}
=1+9/16
$