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

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

(F)=3F/2F+1

We move all terms to the left:

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


Domain of the equation: 2F+1)!=0

F∈R


We get rid of parentheses

F-3F/2F-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

2F^2-5F=0

a = 2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*2}=\frac{0}{4}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*2}=\frac{10}{4}
=2+1/2
$