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

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

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

We move all terms to the left:

1/2x+3-(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

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

We calculate fractions


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

We add all the numbers together, and all the variables

3x/6x^2+(-2x)/6x^2+5=0

We multiply all the terms by the denominator


3x+(-2x)+5*6x^2=0

Wy multiply elements

30x^2+3x+(-2x)=0

We get rid of parentheses

30x^2+3x-2x=0

We add all the numbers together, and all the variables

30x^2+x=0

a = 30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·30·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*30}=\frac{-2}{60}
=-1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*30}=\frac{0}{60}
=0
$