F(x)=5x/3x+2

Solution for F(x)=5x/3x+2 equation:

(F)=5F/3F+2

We move all terms to the left:

(F)-(5F/3F+2)=0


Domain of the equation: 3F+2)!=0

F∈R


We get rid of parentheses

F-5F/3F-2=0

We multiply all the terms by the denominator


F*3F-5F-2*3F=0

We add all the numbers together, and all the variables

-5F+F*3F-2*3F=0

Wy multiply elements

3F^2-5F-6F=0

We add all the numbers together, and all the variables

3F^2-11F=0

a = 3; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·3·0
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*3}=\frac{0}{6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*3}=\frac{22}{6}
=3+2/3
$