X(32-x)=231

Solution for X(32-x)=231 equation:

X(32-X)=231

We move all terms to the left:

X(32-X)-(231)=0

We add all the numbers together, and all the variables

X(-1X+32)-231=0

We multiply parentheses

-1X^2+32X-231=0

a = -1; b = 32; c = -231;
Δ = b2-4ac
Δ = 322-4·(-1)·(-231)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-10}{2*-1}=\frac{-42}{-2}
=+21
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+10}{2*-1}=\frac{-22}{-2}
=+11
$