64=32t-t^2

Solution for 64=32t-t^2 equation:

64=32t-t^2

We move all terms to the left:

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

We get rid of parentheses

t^2-32t+64=0

a = 1; b = -32; c = +64;
Δ = b2-4ac
Δ = -322-4·1·64
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16\sqrt{3}}{2*1}=\frac{32-16\sqrt{3}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16\sqrt{3}}{2*1}=\frac{32+16\sqrt{3}}{2}
$