18=x(18-x)

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

18=x(18-x)

We move all terms to the left:

18-(x(18-x))=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

x^2-18x+18=0

a = 1; b = -18; c = +18;
Δ = b2-4ac
Δ = -182-4·1·18
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{7}}{2*1}=\frac{18-6\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{7}}{2*1}=\frac{18+6\sqrt{7}}{2}
$