0=-16t^2+64t+32

Solution for 0=-16t^2+64t+32 equation:

0=-16t^2+64t+32

We move all terms to the left:

0-(-16t^2+64t+32)=0

We add all the numbers together, and all the variables

-(-16t^2+64t+32)=0

We get rid of parentheses

16t^2-64t-32=0

a = 16; b = -64; c = -32;
Δ = b2-4ac
Δ = -642-4·16·(-32)
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-32\sqrt{6}}{2*16}=\frac{64-32\sqrt{6}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32\sqrt{6}}{2*16}=\frac{64+32\sqrt{6}}{32}
$