50000=x(200-0.2x)

Solution for 50000=x(200-0.2x) equation:

50000=x(200-0.2x)

We move all terms to the left:

50000-(x(200-0.2x))=0

We add all the numbers together, and all the variables

-(x(-0.2x+200))+50000=0


We calculate terms in parentheses: -(x(-0.2x+200)), so:

x(-0.2x+200)

We multiply parentheses

0x^2+200x

We add all the numbers together, and all the variables

x^2+200x

Back to the equation:

-(x^2+200x)


We get rid of parentheses

-x^2-200x+50000=0

We add all the numbers together, and all the variables

-1x^2-200x+50000=0

a = -1; b = -200; c = +50000;
Δ = b2-4ac
Δ = -2002-4·(-1)·50000
Δ = 240000
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:

$\sqrt{\Delta}=\sqrt{240000}=\sqrt{40000*6}=\sqrt{40000}*\sqrt{6}=200\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-200\sqrt{6}}{2*-1}=\frac{200-200\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+200\sqrt{6}}{2*-1}=\frac{200+200\sqrt{6}}{-2}
$