0=32+32t-16t^2

Solution for 0=32+32t-16t^2 equation:

0=32+32t-16t^2

We move all terms to the left:

0-(32+32t-16t^2)=0

We add all the numbers together, and all the variables

-(32+32t-16t^2)=0

We get rid of parentheses

16t^2-32t-32=0

a = 16; b = -32; c = -32;
Δ = b2-4ac
Δ = -322-4·16·(-32)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32\sqrt{3}}{2*16}=\frac{32-32\sqrt{3}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32\sqrt{3}}{2*16}=\frac{32+32\sqrt{3}}{32}
$