(2000-2x)(x)=2000

Solution for (2000-2x)(x)=2000 equation:

(2000-2x)(x)=2000

We move all terms to the left:

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

We add all the numbers together, and all the variables

(-2x+2000)x-2000=0

We multiply parentheses

-2x^2+2000x-2000=0

a = -2; b = 2000; c = -2000;
Δ = b2-4ac
Δ = 20002-4·(-2)·(-2000)
Δ = 3984000
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:

$\sqrt{\Delta}=\sqrt{3984000}=\sqrt{1600*2490}=\sqrt{1600}*\sqrt{2490}=40\sqrt{2490}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2000)-40\sqrt{2490}}{2*-2}=\frac{-2000-40\sqrt{2490}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2000)+40\sqrt{2490}}{2*-2}=\frac{-2000+40\sqrt{2490}}{-4}
$