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

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

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

We move all terms to the left:

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


Domain of the equation: 3(x+1)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(4x-4)/(6x+6)+(-9xx/(6x+6)=0


We calculate terms in parentheses: +(-9xx/(6x+6), so:

-9xx/(6x+6

We multiply all the terms by the denominator


-9xx

Back to the equation:

+(-9xx)


We get rid of parentheses

(4x-4)/(6x+6)-9xx=0

We multiply all the terms by the denominator


(4x-4)-9xx*(6x+6)=0

We multiply parentheses

-54x^2+(4x-4)-54x=0

We get rid of parentheses

-54x^2+4x-54x-4=0

We add all the numbers together, and all the variables

-54x^2-50x-4=0

a = -54; b = -50; c = -4;
Δ = b2-4ac
Δ = -502-4·(-54)·(-4)
Δ = 1636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{409}}{2*-54}=\frac{50-2\sqrt{409}}{-108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{409}}{2*-54}=\frac{50+2\sqrt{409}}{-108}
$