F(x)=x(18-x)

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

(F)=F(18-F)

We move all terms to the left:

(F)-(F(18-F))=0

We add all the numbers together, and all the variables

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


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

F(-1F+18)

We multiply parentheses

-1F^2+18F

Back to the equation:

-(-1F^2+18F)


We get rid of parentheses

1F^2-18F+F=0

We add all the numbers together, and all the variables

F^2-17F=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:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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