H=-16t^2+145t+2

Solution for H=-16t^2+145t+2 equation:

=-16H^2+145H+2

We move all terms to the left:

-(-16H^2+145H+2)=0

We get rid of parentheses

16H^2-145H-2=0

a = 16; b = -145; c = -2;
Δ = b2-4ac
Δ = -1452-4·16·(-2)
Δ = 21153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-145)-\sqrt{21153}}{2*16}=\frac{145-\sqrt{21153}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-145)+\sqrt{21153}}{2*16}=\frac{145+\sqrt{21153}}{32}
$