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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We calculate fractions


6x+(-4x-2)/14x+(-7x)/14x-2-2=0

We add all the numbers together, and all the variables

6x+(-4x-2)/14x+(-7x)/14x-4=0

We multiply all the terms by the denominator


6x*14x+(-4x-2)+(-7x)-4*14x=0

Wy multiply elements

84x^2+(-4x-2)+(-7x)-56x=0

We get rid of parentheses

84x^2-4x-7x-56x-2=0

We add all the numbers together, and all the variables

84x^2-67x-2=0

a = 84; b = -67; c = -2;
Δ = b2-4ac
Δ = -672-4·84·(-2)
Δ = 5161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67)-\sqrt{5161}}{2*84}=\frac{67-\sqrt{5161}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+\sqrt{5161}}{2*84}=\frac{67+\sqrt{5161}}{168}
$