1000-500x^2=x

Solution for 1000-500x^2=x equation:

1000-500x^2=x

We move all terms to the left:

1000-500x^2-(x)=0

We add all the numbers together, and all the variables

-500x^2-1x+1000=0

a = -500; b = -1; c = +1000;
Δ = b2-4ac
Δ = -12-4·(-500)·1000
Δ = 2000001
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{-(-1)-\sqrt{2000001}}{2*-500}=\frac{1-\sqrt{2000001}}{-1000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2000001}}{2*-500}=\frac{1+\sqrt{2000001}}{-1000}
$