F(x)=x/2x-6

Solution for F(x)=x/2x-6 equation:

(F)=F/2F-6

We move all terms to the left:

(F)-(F/2F-6)=0


Domain of the equation: 2F-6)!=0

F∈R


We get rid of parentheses

F-F/2F+6=0

We multiply all the terms by the denominator


F*2F-F+6*2F=0

We add all the numbers together, and all the variables

-1F+F*2F+6*2F=0

Wy multiply elements

2F^2-1F+12F=0

We add all the numbers together, and all the variables

2F^2+11F=0

a = 2; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·2·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*2}=\frac{-22}{4}
=-5+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*2}=\frac{0}{4}
=0
$