H=-16t^2+82t+3

Solution for H=-16t^2+82t+3 equation:

=-16H^2+82H+3

We move all terms to the left:

-(-16H^2+82H+3)=0

We get rid of parentheses

16H^2-82H-3=0

a = 16; b = -82; c = -3;
Δ = b2-4ac
Δ = -822-4·16·(-3)
Δ = 6916
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:

$\sqrt{\Delta}=\sqrt{6916}=\sqrt{4*1729}=\sqrt{4}*\sqrt{1729}=2\sqrt{1729}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1729}}{2*16}=\frac{82-2\sqrt{1729}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1729}}{2*16}=\frac{82+2\sqrt{1729}}{32}
$