-200=-2t-4.9t^2

Solution for -200=-2t-4.9t^2 equation:

-200=-2t-4.9t^2

We move all terms to the left:

-200-(-2t-4.9t^2)=0

We get rid of parentheses

4.9t^2+2t-200=0

a = 4.9; b = 2; c = -200;
Δ = b2-4ac
Δ = 22-4·4.9·(-200)
Δ = 3924
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:

$\sqrt{\Delta}=\sqrt{3924}=\sqrt{4*981}=\sqrt{4}*\sqrt{981}=2\sqrt{981}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{981}}{2*4.9}=\frac{-2-2\sqrt{981}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{981}}{2*4.9}=\frac{-2+2\sqrt{981}}{9.8}
$