2640=16t^2+256t+1680

Solution for 2640=16t^2+256t+1680 equation:

2640=16t^2+256t+1680

We move all terms to the left:

2640-(16t^2+256t+1680)=0

We get rid of parentheses

-16t^2-256t-1680+2640=0

We add all the numbers together, and all the variables

-16t^2-256t+960=0

a = -16; b = -256; c = +960;
Δ = b2-4ac
Δ = -2562-4·(-16)·960
Δ = 126976
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:

$\sqrt{\Delta}=\sqrt{126976}=\sqrt{4096*31}=\sqrt{4096}*\sqrt{31}=64\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-64\sqrt{31}}{2*-16}=\frac{256-64\sqrt{31}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+64\sqrt{31}}{2*-16}=\frac{256+64\sqrt{31}}{-32}
$