X(44-x)=480

Solution for X(44-x)=480 equation:

X(44-X)=480

We move all terms to the left:

X(44-X)-(480)=0

We add all the numbers together, and all the variables

X(-1X+44)-480=0

We multiply parentheses

-1X^2+44X-480=0

a = -1; b = 44; c = -480;
Δ = b2-4ac
Δ = 442-4·(-1)·(-480)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4}{2*-1}=\frac{-48}{-2}
=+24
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4}{2*-1}=\frac{-40}{-2}
=+20
$