0=100+9.5t-4.9t^2

Solution for 0=100+9.5t-4.9t^2 equation:

0=100+9.5t-4.9t^2

We move all terms to the left:

0-(100+9.5t-4.9t^2)=0

We add all the numbers together, and all the variables

-(100+9.5t-4.9t^2)=0

We get rid of parentheses

4.9t^2-9.5t-100=0

a = 4.9; b = -9.5; c = -100;
Δ = b2-4ac
Δ = -9.52-4·4.9·(-100)
Δ = 2050.25
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{-(-9.5)-\sqrt{2050.25}}{2*4.9}=\frac{9.5-\sqrt{2050.25}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.5)+\sqrt{2050.25}}{2*4.9}=\frac{9.5+\sqrt{2050.25}}{9.8}
$