512=-16t^2+192t

Solution for 512=-16t^2+192t equation:

512=-16t^2+192t

We move all terms to the left:

512-(-16t^2+192t)=0

We get rid of parentheses

16t^2-192t+512=0

a = 16; b = -192; c = +512;
Δ = b2-4ac
Δ = -1922-4·16·512
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-64}{2*16}=\frac{128}{32}
=4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+64}{2*16}=\frac{256}{32}
=8
$