4/2x+1=2/3x

Solution for 4/2x+1=2/3x equation:

4/2x+1=2/3x

We move all terms to the left:

4/2x+1-(2/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/2x-(+2/3x)+1=0

We get rid of parentheses

4/2x-2/3x+1=0

We calculate fractions


12x/6x^2+(-4x)/6x^2+1=0

We multiply all the terms by the denominator


12x+(-4x)+1*6x^2=0

Wy multiply elements

6x^2+12x+(-4x)=0

We get rid of parentheses

6x^2+12x-4x=0

We add all the numbers together, and all the variables

6x^2+8x=0

a = 6; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·6·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*6}=\frac{-16}{12}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*6}=\frac{0}{12}
=0
$