x(24-x)=44

Solution for x(24-x)=44 equation:

x(24-x)=44

We move all terms to the left:

x(24-x)-(44)=0

We add all the numbers together, and all the variables

x(-1x+24)-44=0

We multiply parentheses

-1x^2+24x-44=0

a = -1; b = 24; c = -44;
Δ = b2-4ac
Δ = 242-4·(-1)·(-44)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20}{2*-1}=\frac{-44}{-2}
=+22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20}{2*-1}=\frac{-4}{-2}
=+2
$