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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


(3x^2-2x)+(-7x)=0

We get rid of parentheses

3x^2-2x-7x=0

We add all the numbers together, and all the variables

3x^2-9x=0

a = 3; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·3·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*3}=\frac{18}{6}
=3
$