1/7x-1=1/5x+1

Solution for 1/7x-1=1/5x+1 equation:

1/7x-1=1/5x+1

We move all terms to the left:

1/7x-1-(1/5x+1)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

1/7x-1/5x-1-1=0

We calculate fractions


5x/35x^2+(-7x)/35x^2-1-1=0

We add all the numbers together, and all the variables

5x/35x^2+(-7x)/35x^2-2=0

We multiply all the terms by the denominator


5x+(-7x)-2*35x^2=0

Wy multiply elements

-70x^2+5x+(-7x)=0

We get rid of parentheses

-70x^2+5x-7x=0

We add all the numbers together, and all the variables

-70x^2-2x=0

a = -70; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-70)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-70}=\frac{0}{-140}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-70}=\frac{4}{-140}
=-1/35
$