2/3x-1=6/7x

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

2/3x-1=6/7x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


14x/21x^2+(-18x)/21x^2-1=0

We multiply all the terms by the denominator


14x+(-18x)-1*21x^2=0

Wy multiply elements

-21x^2+14x+(-18x)=0

We get rid of parentheses

-21x^2+14x-18x=0

We add all the numbers together, and all the variables

-21x^2-4x=0

a = -21; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-21)·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*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-21}=\frac{8}{-42}
=-4/21
$