0=5t-4.9t^2-0.5

Solution for 0=5t-4.9t^2-0.5 equation:

0=5t-4.9t^2-0.5

We move all terms to the left:

0-(5t-4.9t^2-0.5)=0

We add all the numbers together, and all the variables

-(5t-4.9t^2-0.5)=0

We get rid of parentheses

4.9t^2-5t+0.5=0

a = 4.9; b = -5; c = +0.5;
Δ = b2-4ac
Δ = -52-4·4.9·0.5
Δ = 15.2
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)-\sqrt{15.2}}{2*4.9}=\frac{5-\sqrt{15.2}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{15.2}}{2*4.9}=\frac{5+\sqrt{15.2}}{9.8}
$