0=-4.9t^2+24.6t+50.5

Solution for 0=-4.9t^2+24.6t+50.5 equation:

0=-4.9t^2+24.6t+50.5

We move all terms to the left:

0-(-4.9t^2+24.6t+50.5)=0

We add all the numbers together, and all the variables

-(-4.9t^2+24.6t+50.5)=0

We get rid of parentheses

4.9t^2-24.6t-50.5=0

a = 4.9; b = -24.6; c = -50.5;
Δ = b2-4ac
Δ = -24.62-4·4.9·(-50.5)
Δ = 1594.96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24.6)-\sqrt{1594.96}}{2*4.9}=\frac{24.6-\sqrt{1594.96}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24.6)+\sqrt{1594.96}}{2*4.9}=\frac{24.6+\sqrt{1594.96}}{9.8}
$