2/3x+6=3/2x-2

Solution for 2/3x+6=3/2x-2 equation:

2/3x+6=3/2x-2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-2)!=0

x∈R


We get rid of parentheses

2/3x-3/2x+2+6=0

We calculate fractions


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

We add all the numbers together, and all the variables

4x/6x^2+(-9x)/6x^2+8=0

We multiply all the terms by the denominator


4x+(-9x)+8*6x^2=0

Wy multiply elements

48x^2+4x+(-9x)=0

We get rid of parentheses

48x^2+4x-9x=0

We add all the numbers together, and all the variables

48x^2-5x=0

a = 48; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·48·0
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*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*48}=\frac{10}{96}
=5/48
$