20=96t-16t^2

Solution for 20=96t-16t^2 equation:

20=96t-16t^2

We move all terms to the left:

20-(96t-16t^2)=0

We get rid of parentheses

16t^2-96t+20=0

a = 16; b = -96; c = +20;
Δ = b2-4ac
Δ = -962-4·16·20
Δ = 7936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7936}=\sqrt{256*31}=\sqrt{256}*\sqrt{31}=16\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{31}}{2*16}=\frac{96-16\sqrt{31}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{31}}{2*16}=\frac{96+16\sqrt{31}}{32}
$