2x/x+3+1/12=3/2x-1

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Solution for 2x/x+3+1/12=3/2x-1 equation:



2x/x+3+1/12=3/2x-1
We move all terms to the left:
2x/x+3+1/12-(3/2x-1)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x-1)!=0
x∈R
We get rid of parentheses
2x/x-3/2x+1+3+1/12=0
We calculate fractions
48x^2/24x^2+4x^2/24x^2+(-36x)/24x^2+1+3=0
We add all the numbers together, and all the variables
48x^2/24x^2+4x^2/24x^2+(-36x)/24x^2+4=0
We multiply all the terms by the denominator
48x^2+4x^2+(-36x)+4*24x^2=0
We add all the numbers together, and all the variables
52x^2+(-36x)+4*24x^2=0
Wy multiply elements
52x^2+96x^2+(-36x)=0
We get rid of parentheses
52x^2+96x^2-36x=0
We add all the numbers together, and all the variables
148x^2-36x=0
a = 148; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·148·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*148}=\frac{0}{296} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*148}=\frac{72}{296} =9/37 $

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