X(47-x)=550

Solution for X(47-x)=550 equation:

X(47-X)=550

We move all terms to the left:

X(47-X)-(550)=0

We add all the numbers together, and all the variables

X(-1X+47)-550=0

We multiply parentheses

-1X^2+47X-550=0

a = -1; b = 47; c = -550;
Δ = b2-4ac
Δ = 472-4·(-1)·(-550)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-3}{2*-1}=\frac{-50}{-2}
=+25
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+3}{2*-1}=\frac{-44}{-2}
=+22
$