x=500x-50x^2

Solution for x=500x-50x^2 equation:

x=500x-50x^2

We move all terms to the left:

x-(500x-50x^2)=0

We get rid of parentheses

50x^2-500x+x=0

We add all the numbers together, and all the variables

50x^2-499x=0

a = 50; b = -499; c = 0;
Δ = b2-4ac
Δ = -4992-4·50·0
Δ = 249001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{249001}=499$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-499)-499}{2*50}=\frac{0}{100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-499)+499}{2*50}=\frac{998}{100}
=9+49/50
$