3/7x+1/3=1/3x+1

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Solution for 3/7x+1/3=1/3x+1 equation:



3/7x+1/3=1/3x+1
We move all terms to the left:
3/7x+1/3-(1/3x+1)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 3x+1)!=0
x∈R
We get rid of parentheses
3/7x-1/3x-1+1/3=0
We calculate fractions
81x/189x^2+(-7x)/189x^2+7x/189x^2-1=0
We multiply all the terms by the denominator
81x+(-7x)+7x-1*189x^2=0
We add all the numbers together, and all the variables
88x+(-7x)-1*189x^2=0
Wy multiply elements
-189x^2+88x+(-7x)=0
We get rid of parentheses
-189x^2+88x-7x=0
We add all the numbers together, and all the variables
-189x^2+81x=0
a = -189; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·(-189)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*-189}=\frac{-162}{-378} =3/7 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*-189}=\frac{0}{-378} =0 $

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