0=-16t2+64t+512

Solution for 0=-16t2+64t+512 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

16t^2-64t-512=0

a = 16; b = -64; c = -512;
Δ = b2-4ac
Δ = -642-4·16·(-512)
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-192}{2*16}=\frac{-128}{32}
=-4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+192}{2*16}=\frac{256}{32}
=8
$