T=20+96t-9.8t^2

Solution for T=20+96t-9.8t^2 equation:

=20+96T-9.8T^2

We move all terms to the left:

-(20+96T-9.8T^2)=0

We get rid of parentheses

9.8T^2-96T-20=0

a = 9.8; b = -96; c = -20;
Δ = b2-4ac
Δ = -962-4·9.8·(-20)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-100}{2*9.8}=\frac{-4}{19.6}
=-4/19.6
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+100}{2*9.8}=\frac{196}{19.6}
=10
$