F(x)=x/9x+6

Solution for F(x)=x/9x+6 equation:

(F)=F/9F+6

We move all terms to the left:

(F)-(F/9F+6)=0


Domain of the equation: 9F+6)!=0

F∈R


We get rid of parentheses

F-F/9F-6=0

We multiply all the terms by the denominator


F*9F-F-6*9F=0

We add all the numbers together, and all the variables

-1F+F*9F-6*9F=0

Wy multiply elements

9F^2-1F-54F=0

We add all the numbers together, and all the variables

9F^2-55F=0

a = 9; b = -55; c = 0;
Δ = b2-4ac
Δ = -552-4·9·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-55}{2*9}=\frac{0}{18}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+55}{2*9}=\frac{110}{18}
=6+1/9
$