F(x)=x*(26-2x)

Solution for F(x)=x*(26-2x) equation:

(F)=F(26-2F)

We move all terms to the left:

(F)-(F(26-2F))=0

We add all the numbers together, and all the variables

F-(F(-2F+26))=0


We calculate terms in parentheses: -(F(-2F+26)), so:

F(-2F+26)

We multiply parentheses

-2F^2+26F

Back to the equation:

-(-2F^2+26F)


We get rid of parentheses

2F^2-26F+F=0

We add all the numbers together, and all the variables

2F^2-25F=0

a = 2; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·2·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*2}=\frac{0}{4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*2}=\frac{50}{4}
=12+1/2
$