0=8t+19.6t^2

Solution for 0=8t+19.6t^2 equation:

0=8t+19.6t^2

We move all terms to the left:

0-(8t+19.6t^2)=0

We add all the numbers together, and all the variables

-(8t+19.6t^2)=0

We get rid of parentheses

-19.6t^2-8t=0

a = -19.6; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-19.6)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-19.6}=\frac{0}{-39.2}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-19.6}=\frac{16}{-39.2}
=-16/39.2
$