32+64t-16t^2=0

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

32+64t-16t^2=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}
$