0=3+24.5t-4.9t^2

Solution for 0=3+24.5t-4.9t^2 equation:

0=3+24.5t-4.9t^2

We move all terms to the left:

0-(3+24.5t-4.9t^2)=0

We add all the numbers together, and all the variables

-(3+24.5t-4.9t^2)=0

We get rid of parentheses

4.9t^2-24.5t-3=0

a = 4.9; b = -24.5; c = -3;
Δ = b2-4ac
Δ = -24.52-4·4.9·(-3)
Δ = 659.05
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{659.05}}{2*4.9}=\frac{24.5-\sqrt{659.05}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24.5)+\sqrt{659.05}}{2*4.9}=\frac{24.5+\sqrt{659.05}}{9.8}
$