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

We add all the numbers together, and all the variables

5x-5*6x^2=0

Wy multiply elements

-30x^2+5x=0

a = -30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-30)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-30}=\frac{-10}{-60}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-30}=\frac{0}{-60}
=0
$