X(24-x)=63

Solution for X(24-x)=63 equation:

X(24-X)=63

We move all terms to the left:

X(24-X)-(63)=0

We add all the numbers together, and all the variables

X(-1X+24)-63=0

We multiply parentheses

-1X^2+24X-63=0

a = -1; b = 24; c = -63;
Δ = b2-4ac
Δ = 242-4·(-1)·(-63)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-18}{2*-1}=\frac{-42}{-2}
=+21
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+18}{2*-1}=\frac{-6}{-2}
=+3
$