X(-x+40)-200=0

Solution for X(-x+40)-200=0 equation:

X(-X+40)-200=0

We add all the numbers together, and all the variables

X(-1X+40)-200=0

We multiply parentheses

-1X^2+40X-200=0

a = -1; b = 40; c = -200;
Δ = b2-4ac
Δ = 402-4·(-1)·(-200)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-20\sqrt{2}}{2*-1}=\frac{-40-20\sqrt{2}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+20\sqrt{2}}{2*-1}=\frac{-40+20\sqrt{2}}{-2}
$