0=-4.9t^2+t+109.2

Solution for 0=-4.9t^2+t+109.2 equation:

0=-4.9t^2+t+109.2

We move all terms to the left:

0-(-4.9t^2+t+109.2)=0

We add all the numbers together, and all the variables

-(-4.9t^2+t+109.2)=0

We get rid of parentheses

4.9t^2-t-109.2=0

We add all the numbers together, and all the variables

4.9t^2-1t-109.2=0

a = 4.9; b = -1; c = -109.2;
Δ = b2-4ac
Δ = -12-4·4.9·(-109.2)
Δ = 2141.32
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{-(-1)-\sqrt{2141.32}}{2*4.9}=\frac{1-\sqrt{2141.32}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2141.32}}{2*4.9}=\frac{1+\sqrt{2141.32}}{9.8}
$