2/7x=1/3x-2

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

2/7x=1/3x-2

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


6x+(-7x)+2*21x^2=0

Wy multiply elements

42x^2+6x+(-7x)=0

We get rid of parentheses

42x^2+6x-7x=0

We add all the numbers together, and all the variables

42x^2-1x=0

a = 42; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·42·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*42}=\frac{0}{84}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*42}=\frac{2}{84}
=1/42
$