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

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

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

We move all terms to the left:

1/3x-6-(1/7x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x+2)!=0

x∈R


We get rid of parentheses

1/3x-1/7x-2-6=0

We calculate fractions


7x/21x^2+(-3x)/21x^2-2-6=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
$