0=500-9x-4.9x^2

Solution for 0=500-9x-4.9x^2 equation:

0=500-9x-4.9x^2

We move all terms to the left:

0-(500-9x-4.9x^2)=0

We add all the numbers together, and all the variables

-(500-9x-4.9x^2)=0

We get rid of parentheses

4.9x^2+9x-500=0

a = 4.9; b = 9; c = -500;
Δ = b2-4ac
Δ = 92-4·4.9·(-500)
Δ = 9881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{9881}}{2*4.9}=\frac{-9-\sqrt{9881}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{9881}}{2*4.9}=\frac{-9+\sqrt{9881}}{9.8}
$