200=-16t^2-20t+400

Solution for 200=-16t^2-20t+400 equation:

200=-16t^2-20t+400

We move all terms to the left:

200-(-16t^2-20t+400)=0

We get rid of parentheses

16t^2+20t-400+200=0

We add all the numbers together, and all the variables

16t^2+20t-200=0

a = 16; b = 20; c = -200;
Δ = b2-4ac
Δ = 202-4·16·(-200)
Δ = 13200
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:

$\sqrt{\Delta}=\sqrt{13200}=\sqrt{400*33}=\sqrt{400}*\sqrt{33}=20\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{33}}{2*16}=\frac{-20-20\sqrt{33}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{33}}{2*16}=\frac{-20+20\sqrt{33}}{32}
$