H(t)=-16t^2+101t+10

Solution for H(t)=-16t^2+101t+10 equation:

(H)=-16H^2+101H+10

We move all terms to the left:

(H)-(-16H^2+101H+10)=0

We get rid of parentheses

16H^2-101H+H-10=0

We add all the numbers together, and all the variables

16H^2-100H-10=0

a = 16; b = -100; c = -10;
Δ = b2-4ac
Δ = -1002-4·16·(-10)
Δ = 10640
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:

$\sqrt{\Delta}=\sqrt{10640}=\sqrt{16*665}=\sqrt{16}*\sqrt{665}=4\sqrt{665}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{665}}{2*16}=\frac{100-4\sqrt{665}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{665}}{2*16}=\frac{100+4\sqrt{665}}{32}
$