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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*3x+1*3x-1*3x+6=0

Wy multiply elements

-6x^2+3x-3x+6=0

We add all the numbers together, and all the variables

-6x^2+6=0

a = -6; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-6)·6
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-6}=\frac{12}{-12}
=-1
$