5000=2000x-2x^2

Solution for 5000=2000x-2x^2 equation:

5000=2000x-2x^2

We move all terms to the left:

5000-(2000x-2x^2)=0

We get rid of parentheses

2x^2-2000x+5000=0

a = 2; b = -2000; c = +5000;
Δ = b2-4ac
Δ = -20002-4·2·5000
Δ = 3960000
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:

$\sqrt{\Delta}=\sqrt{3960000}=\sqrt{360000*11}=\sqrt{360000}*\sqrt{11}=600\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2000)-600\sqrt{11}}{2*2}=\frac{2000-600\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2000)+600\sqrt{11}}{2*2}=\frac{2000+600\sqrt{11}}{4}
$