4/2x+3=3/3x+2

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

4/2x+3=3/3x+2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


12x/6x^2+(-6x)/6x^2-2+3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+6x=0

a = 6; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·6·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*6}=\frac{0}{12}
=0
$