19.6=-4.9t^2+24.5t+S

Solution for 19.6=-4.9t^2+24.5t+S equation:

19.6=-4.9t^2+24.5t+

We move all terms to the left:

19.6-(-4.9t^2+24.5t+)=0

We get rid of parentheses

4.9t^2-24.5t+19.6-=0

We add all the numbers together, and all the variables

4.9t^2-24.5t=0

a = 4.9; b = -24.5; c = 0;
Δ = b2-4ac
Δ = -24.52-4·4.9·0
Δ = 600.25
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{-(-24.5)-\sqrt{600.25}}{2*4.9}=\frac{24.5-\sqrt{600.25}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24.5)+\sqrt{600.25}}{2*4.9}=\frac{24.5+\sqrt{600.25}}{9.8}
$