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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/1029x^2+(-686x)/1029x^2+3x/1029x^2+1=0

We multiply all the terms by the denominator


6x+(-686x)+3x+1*1029x^2=0

We add all the numbers together, and all the variables

9x+(-686x)+1*1029x^2=0

Wy multiply elements

1029x^2+9x+(-686x)=0

We get rid of parentheses

1029x^2+9x-686x=0

We add all the numbers together, and all the variables

1029x^2-677x=0

a = 1029; b = -677; c = 0;
Δ = b2-4ac
Δ = -6772-4·1029·0
Δ = 458329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{458329}=677$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-677)-677}{2*1029}=\frac{0}{2058}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-677)+677}{2*1029}=\frac{1354}{2058}
=677/1029
$