0=96t+16t^2

Solution for 0=96t+16t^2 equation:

0=96t+16t^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-16t^2-96t=0

a = -16; b = -96; c = 0;
Δ = b2-4ac
Δ = -962-4·(-16)·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-96}{2*-16}=\frac{0}{-32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+96}{2*-16}=\frac{192}{-32}
=-6
$