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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-9x)/6x^2+(-4x)/6x^2+3+2=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^2-13x=0

a = 30; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·30·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*30}=\frac{26}{60}
=13/30
$