2/2x-1=4/3x+1

Solution for 2/2x-1=4/3x+1 equation:

2/2x-1=4/3x+1

We move all terms to the left:

2/2x-1-(4/3x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/2x-4/3x-1-1=0

We calculate fractions


6x/6x^2+(-8x)/6x^2-1-1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+6x+(-8x)=0

We get rid of parentheses

-12x^2+6x-8x=0

We add all the numbers together, and all the variables

-12x^2-2x=0

a = -12; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-12)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-12}=\frac{4}{-24}
=-1/6
$