64t=-16t^2+64

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

64t=-16t^2+64

We move all terms to the left:

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

We get rid of parentheses

16t^2+64t-64=0

a = 16; b = 64; c = -64;
Δ = b2-4ac
Δ = 642-4·16·(-64)
Δ = 8192
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:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64\sqrt{2}}{2*16}=\frac{-64-64\sqrt{2}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64\sqrt{2}}{2*16}=\frac{-64+64\sqrt{2}}{32}
$