0=23.839+7.5t-4.9t^2

Solution for 0=23.839+7.5t-4.9t^2 equation:

0=23.839+7.5t-4.9t^2

We move all terms to the left:

0-(23.839+7.5t-4.9t^2)=0

We add all the numbers together, and all the variables

-(23.839+7.5t-4.9t^2)=0

We get rid of parentheses

4.9t^2-7.5t-23.839=0

a = 4.9; b = -7.5; c = -23.839;
Δ = b2-4ac
Δ = -7.52-4·4.9·(-23.839)
Δ = 523.4944
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{-(-7.5)-\sqrt{523.4944}}{2*4.9}=\frac{7.5-\sqrt{523.4944}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{523.4944}}{2*4.9}=\frac{7.5+\sqrt{523.4944}}{9.8}
$