1/3x-2=1/7x+6

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Solution for 1/3x-2=1/7x+6 equation:



1/3x-2=1/7x+6
We move all terms to the left:
1/3x-2-(1/7x+6)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 7x+6)!=0
x∈R
We get rid of parentheses
1/3x-1/7x-6-2=0
We calculate fractions
7x/21x^2+(-3x)/21x^2-6-2=0
We add all the numbers together, and all the variables
7x/21x^2+(-3x)/21x^2-8=0
We multiply all the terms by the denominator
7x+(-3x)-8*21x^2=0
Wy multiply elements
-168x^2+7x+(-3x)=0
We get rid of parentheses
-168x^2+7x-3x=0
We add all the numbers together, and all the variables
-168x^2+4x=0
a = -168; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-168)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-168}=\frac{-8}{-336} =1/42 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-168}=\frac{0}{-336} =0 $

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