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

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



2/3x-1=1/2x+1
We move all terms to the left:
2/3x-1-(1/2x+1)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x+1)!=0
x∈R
We get rid of parentheses
2/3x-1/2x-1-1=0
We calculate fractions
4x/6x^2+(-3x)/6x^2-1-1=0
We add all the numbers together, and all the variables
4x/6x^2+(-3x)/6x^2-2=0
We multiply all the terms by the denominator
4x+(-3x)-2*6x^2=0
Wy multiply elements
-12x^2+4x+(-3x)=0
We get rid of parentheses
-12x^2+4x-3x=0
We add all the numbers together, and all the variables
-12x^2+x=0
a = -12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-12)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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

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