4x(4000-x)=200

Solution for 4x(4000-x)=200 equation:

4x(4000-x)=200

We move all terms to the left:

4x(4000-x)-(200)=0

We add all the numbers together, and all the variables

4x(-1x+4000)-200=0

We multiply parentheses

-4x^2+16000x-200=0

a = -4; b = 16000; c = -200;
Δ = b2-4ac
Δ = 160002-4·(-4)·(-200)
Δ = 255996800
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:

$\sqrt{\Delta}=\sqrt{255996800}=\sqrt{1600*159998}=\sqrt{1600}*\sqrt{159998}=40\sqrt{159998}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16000)-40\sqrt{159998}}{2*-4}=\frac{-16000-40\sqrt{159998}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16000)+40\sqrt{159998}}{2*-4}=\frac{-16000+40\sqrt{159998}}{-8}
$