1900=250t+4.9t^2

Solution for 1900=250t+4.9t^2 equation:

1900=250t+4.9t^2

We move all terms to the left:

1900-(250t+4.9t^2)=0

We get rid of parentheses

-4.9t^2-250t+1900=0

a = -4.9; b = -250; c = +1900;
Δ = b2-4ac
Δ = -2502-4·(-4.9)·1900
Δ = 99740
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:

$\sqrt{\Delta}=\sqrt{99740}=\sqrt{4*24935}=\sqrt{4}*\sqrt{24935}=2\sqrt{24935}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-2\sqrt{24935}}{2*-4.9}=\frac{250-2\sqrt{24935}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+2\sqrt{24935}}{2*-4.9}=\frac{250+2\sqrt{24935}}{-9.8}
$