0=50+50t-4.9t^2

Solution for 0=50+50t-4.9t^2 equation:

0=50+50t-4.9t^2

We move all terms to the left:

0-(50+50t-4.9t^2)=0

We add all the numbers together, and all the variables

-(50+50t-4.9t^2)=0

We get rid of parentheses

4.9t^2-50t-50=0

a = 4.9; b = -50; c = -50;
Δ = b2-4ac
Δ = -502-4·4.9·(-50)
Δ = 3480
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:

$\sqrt{\Delta}=\sqrt{3480}=\sqrt{4*870}=\sqrt{4}*\sqrt{870}=2\sqrt{870}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{870}}{2*4.9}=\frac{50-2\sqrt{870}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{870}}{2*4.9}=\frac{50+2\sqrt{870}}{9.8}
$