0=102+5.39t-4.9t^2

Solution for 0=102+5.39t-4.9t^2 equation:

0=102+5.39t-4.9t^2

We move all terms to the left:

0-(102+5.39t-4.9t^2)=0

We add all the numbers together, and all the variables

-(102+5.39t-4.9t^2)=0

We get rid of parentheses

4.9t^2-5.39t-102=0

a = 4.9; b = -5.39; c = -102;
Δ = b2-4ac
Δ = -5.392-4·4.9·(-102)
Δ = 2028.2521
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{-(-5.39)-\sqrt{2028.2521}}{2*4.9}=\frac{5.39-\sqrt{2028.2521}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.39)+\sqrt{2028.2521}}{2*4.9}=\frac{5.39+\sqrt{2028.2521}}{9.8}
$