1/7x-1=3/x

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

1/7x-1=3/x

We move all terms to the left:

1/7x-1-(3/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

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

We get rid of parentheses

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

We calculate fractions


x/7x^2+(-21x)/7x^2-1=0

We multiply all the terms by the denominator


x+(-21x)-1*7x^2=0

Wy multiply elements

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

We get rid of parentheses

-7x^2+x-21x=0

We add all the numbers together, and all the variables

-7x^2-20x=0

a = -7; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-7)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-7}=\frac{40}{-14}
=-2+6/7
$