2=-16t^2+64t+512

Solution for 2=-16t^2+64t+512 equation:

2=-16t^2+64t+512

We move all terms to the left:

2-(-16t^2+64t+512)=0

We get rid of parentheses

16t^2-64t-512+2=0

We add all the numbers together, and all the variables

16t^2-64t-510=0

a = 16; b = -64; c = -510;
Δ = b2-4ac
Δ = -642-4·16·(-510)
Δ = 36736
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:

$\sqrt{\Delta}=\sqrt{36736}=\sqrt{64*574}=\sqrt{64}*\sqrt{574}=8\sqrt{574}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{574}}{2*16}=\frac{64-8\sqrt{574}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{574}}{2*16}=\frac{64+8\sqrt{574}}{32}
$