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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We calculate fractions


6x+(-6x)/21x+(-7x)/21x-2-2=0

We add all the numbers together, and all the variables

6x+(-6x)/21x+(-7x)/21x-4=0

We multiply all the terms by the denominator


6x*21x+(-6x)+(-7x)-4*21x=0

Wy multiply elements

126x^2+(-6x)+(-7x)-84x=0

We get rid of parentheses

126x^2-6x-7x-84x=0

We add all the numbers together, and all the variables

126x^2-97x=0

a = 126; b = -97; c = 0;
Δ = b2-4ac
Δ = -972-4·126·0
Δ = 9409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9409}=97$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-97)-97}{2*126}=\frac{0}{252}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+97}{2*126}=\frac{194}{252}
=97/126
$