0=16t^2+80t-1600

Solution for 0=16t^2+80t-1600 equation:

0=16t^2+80t-1600

We move all terms to the left:

0-(16t^2+80t-1600)=0

We add all the numbers together, and all the variables

-(16t^2+80t-1600)=0

We get rid of parentheses

-16t^2-80t+1600=0

a = -16; b = -80; c = +1600;
Δ = b2-4ac
Δ = -802-4·(-16)·1600
Δ = 108800
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:

$\sqrt{\Delta}=\sqrt{108800}=\sqrt{6400*17}=\sqrt{6400}*\sqrt{17}=80\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80\sqrt{17}}{2*-16}=\frac{80-80\sqrt{17}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80\sqrt{17}}{2*-16}=\frac{80+80\sqrt{17}}{-32}
$