1/3x+1=3/2x

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



1/3x+1=3/2x
We move all terms to the left:
1/3x+1-(3/2x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/3x-(+3/2x)+1=0
We get rid of parentheses
1/3x-3/2x+1=0
We calculate fractions
2x/6x^2+(-9x)/6x^2+1=0
We multiply all the terms by the denominator
2x+(-9x)+1*6x^2=0
Wy multiply elements
6x^2+2x+(-9x)=0
We get rid of parentheses
6x^2+2x-9x=0
We add all the numbers together, and all the variables
6x^2-7x=0
a = 6; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·6·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*6}=\frac{0}{12} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*6}=\frac{14}{12} =1+1/6 $

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