X=x(18-x)

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

X=X(18-X)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(X(-1X+18)), so:

X(-1X+18)

We multiply parentheses

-1X^2+18X

Back to the equation:

-(-1X^2+18X)


We get rid of parentheses

1X^2-18X+X=0

We add all the numbers together, and all the variables

X^2-17X=0

a = 1; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·1·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*1}=\frac{34}{2}
=17
$