x=1000-500x2

Solution for x=1000-500x2 equation:

x=1000-500x^2

We move all terms to the left:

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

We get rid of parentheses

500x^2+x-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}
$