H(t)=-16t^2+140t+2

Solution for H(t)=-16t^2+140t+2 equation:

(H)=-16H^2+140H+2

We move all terms to the left:

(H)-(-16H^2+140H+2)=0

We get rid of parentheses

16H^2-140H+H-2=0

We add all the numbers together, and all the variables

16H^2-139H-2=0

a = 16; b = -139; c = -2;
Δ = b2-4ac
Δ = -1392-4·16·(-2)
Δ = 19449
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:

$\sqrt{\Delta}=\sqrt{19449}=\sqrt{9*2161}=\sqrt{9}*\sqrt{2161}=3\sqrt{2161}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-139)-3\sqrt{2161}}{2*16}=\frac{139-3\sqrt{2161}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-139)+3\sqrt{2161}}{2*16}=\frac{139+3\sqrt{2161}}{32}
$