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

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



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

We move all terms to the left:

3/2x-3-(2/3x+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

3/2x-2/3x-2-3=0

We calculate fractions


9x/6x^2+(-4x)/6x^2-2-3=0

We add all the numbers together, and all the variables

9x/6x^2+(-4x)/6x^2-5=0

We multiply all the terms by the denominator


9x+(-4x)-5*6x^2=0

Wy multiply elements

-30x^2+9x+(-4x)=0

We get rid of parentheses

-30x^2+9x-4x=0

We add all the numbers together, and all the variables

-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
$

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