1000=500x-x^2

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

1000=500x-x^2

We move all terms to the left:

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

We get rid of parentheses

x^2-500x+1000=0

a = 1; b = -500; c = +1000;
Δ = b2-4ac
Δ = -5002-4·1·1000
Δ = 246000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{246000}=\sqrt{400*615}=\sqrt{400}*\sqrt{615}=20\sqrt{615}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-20\sqrt{615}}{2*1}=\frac{500-20\sqrt{615}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+20\sqrt{615}}{2*1}=\frac{500+20\sqrt{615}}{2}
$