X+3/2x+3=x+1/3x+2

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

X+3/2X+3=X+1/3X+2

We move all terms to the left:

X+3/2X+3-(X+1/3X+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

X+3/2X-X-1/3X-2+3=0

We calculate fractions


X-X+9X/6X^2+(-2X)/6X^2-2+3=0

We add all the numbers together, and all the variables

9X/6X^2+(-2X)/6X^2+1=0

We multiply all the terms by the denominator


9X+(-2X)+1*6X^2=0

Wy multiply elements

6X^2+9X+(-2X)=0

We get rid of parentheses

6X^2+9X-2X=0

We add all the numbers together, and all the variables

6X^2+7X=0

a = 6; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·6·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*6}=\frac{-14}{12}
=-1+1/6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*6}=\frac{0}{12}
=0
$