500x(20-x)=40000

Solution for 500x(20-x)=40000 equation:

500x(20-x)=40000

We move all terms to the left:

500x(20-x)-(40000)=0

We add all the numbers together, and all the variables

500x(-1x+20)-40000=0

We multiply parentheses

-500x^2+10000x-40000=0

a = -500; b = 10000; c = -40000;
Δ = b2-4ac
Δ = 100002-4·(-500)·(-40000)
Δ = 20000000
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:

$\sqrt{\Delta}=\sqrt{20000000}=\sqrt{4000000*5}=\sqrt{4000000}*\sqrt{5}=2000\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10000)-2000\sqrt{5}}{2*-500}=\frac{-10000-2000\sqrt{5}}{-1000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10000)+2000\sqrt{5}}{2*-500}=\frac{-10000+2000\sqrt{5}}{-1000}
$