-200=-16t^2+200t

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

-200=-16t^2+200t

We move all terms to the left:

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

We get rid of parentheses

16t^2-200t-200=0

a = 16; b = -200; c = -200;
Δ = b2-4ac
Δ = -2002-4·16·(-200)
Δ = 52800
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:

$\sqrt{\Delta}=\sqrt{52800}=\sqrt{1600*33}=\sqrt{1600}*\sqrt{33}=40\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{33}}{2*16}=\frac{200-40\sqrt{33}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{33}}{2*16}=\frac{200+40\sqrt{33}}{32}
$