0=12+96t-16t^2

Solution for 0=12+96t-16t^2 equation:

0=12+96t-16t^2

We move all terms to the left:

0-(12+96t-16t^2)=0

We add all the numbers together, and all the variables

-(12+96t-16t^2)=0

We get rid of parentheses

16t^2-96t-12=0

a = 16; b = -96; c = -12;
Δ = b2-4ac
Δ = -962-4·16·(-12)
Δ = 9984
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:

$\sqrt{\Delta}=\sqrt{9984}=\sqrt{256*39}=\sqrt{256}*\sqrt{39}=16\sqrt{39}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{39}}{2*16}=\frac{96-16\sqrt{39}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{39}}{2*16}=\frac{96+16\sqrt{39}}{32}
$