X(140-x)=4000

Solution for X(140-x)=4000 equation:

X(140-X)=4000

We move all terms to the left:

X(140-X)-(4000)=0

We add all the numbers together, and all the variables

X(-1X+140)-4000=0

We multiply parentheses

-1X^2+140X-4000=0

a = -1; b = 140; c = -4000;
Δ = b2-4ac
Δ = 1402-4·(-1)·(-4000)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-60}{2*-1}=\frac{-200}{-2}
=+100
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+60}{2*-1}=\frac{-80}{-2}
=+40
$