X*(18-x)=54

Solution for X*(18-x)=54 equation:

X(18-X)=54

We move all terms to the left:

X(18-X)-(54)=0

We add all the numbers together, and all the variables

X(-1X+18)-54=0

We multiply parentheses

-1X^2+18X-54=0

a = -1; b = 18; c = -54;
Δ = b2-4ac
Δ = 182-4·(-1)·(-54)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{3}}{2*-1}=\frac{-18-6\sqrt{3}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{3}}{2*-1}=\frac{-18+6\sqrt{3}}{-2}
$