F(x)=x(9-x)

Solution for F(x)=x(9-x) equation:

(F)=F(9-F)

We move all terms to the left:

(F)-(F(9-F))=0

We add all the numbers together, and all the variables

F-(F(-1F+9))=0


We calculate terms in parentheses: -(F(-1F+9)), so:

F(-1F+9)

We multiply parentheses

-1F^2+9F

Back to the equation:

-(-1F^2+9F)


We get rid of parentheses

1F^2-9F+F=0

We add all the numbers together, and all the variables

F^2-8F=0

a = 1; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·1·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*1}=\frac{16}{2}
=8
$