0=-16t^2+200t-500

Solution for 0=-16t^2+200t-500 equation:

0=-16t^2+200t-500

We move all terms to the left:

0-(-16t^2+200t-500)=0

We add all the numbers together, and all the variables

-(-16t^2+200t-500)=0

We get rid of parentheses

16t^2-200t+500=0

a = 16; b = -200; c = +500;
Δ = b2-4ac
Δ = -2002-4·16·500
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{5}}{2*16}=\frac{200-40\sqrt{5}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{5}}{2*16}=\frac{200+40\sqrt{5}}{32}
$