F(x)=2x/3x-1

Solution for F(x)=2x/3x-1 equation:

(F)=2F/3F-1

We move all terms to the left:

(F)-(2F/3F-1)=0


Domain of the equation: 3F-1)!=0

F∈R


We get rid of parentheses

F-2F/3F+1=0

We multiply all the terms by the denominator


F*3F-2F+1*3F=0

We add all the numbers together, and all the variables

-2F+F*3F+1*3F=0

Wy multiply elements

3F^2-2F+3F=0

We add all the numbers together, and all the variables

3F^2+F=0

a = 3; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·3·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*3}=\frac{-2}{6}
=-1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*3}=\frac{0}{6}
=0
$