96=16t+16t^2

Solution for 96=16t+16t^2 equation:

96=16t+16t^2

We move all terms to the left:

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

We get rid of parentheses

-16t^2-16t+96=0

a = -16; b = -16; c = +96;
Δ = b2-4ac
Δ = -162-4·(-16)·96
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-80}{2*-16}=\frac{-64}{-32}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+80}{2*-16}=\frac{96}{-32}
=-3
$