0=40-9.8t^2-9.8t

Solution for 0=40-9.8t^2-9.8t equation:

0=40-9.8t^2-9.8t

We move all terms to the left:

0-(40-9.8t^2-9.8t)=0

We add all the numbers together, and all the variables

-(40-9.8t^2-9.8t)=0

We get rid of parentheses

9.8t^2+9.8t-40=0

a = 9.8; b = 9.8; c = -40;
Δ = b2-4ac
Δ = 9.82-4·9.8·(-40)
Δ = 1664.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9.8)-\sqrt{1664.04}}{2*9.8}=\frac{-9.8-\sqrt{1664.04}}{19.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.8)+\sqrt{1664.04}}{2*9.8}=\frac{-9.8+\sqrt{1664.04}}{19.6}
$