5/6x-7=1/x-1

Solution for 5/6x-7=1/x-1 equation:

5/6x-7=1/x-1

We move all terms to the left:

5/6x-7-(1/x-1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/6x-1/x+1-7=0

We calculate fractions


5x/6x^2+(-6x)/6x^2+1-7=0

We add all the numbers together, and all the variables

5x/6x^2+(-6x)/6x^2-6=0

We multiply all the terms by the denominator


5x+(-6x)-6*6x^2=0

Wy multiply elements

-36x^2+5x+(-6x)=0

We get rid of parentheses

-36x^2+5x-6x=0

We add all the numbers together, and all the variables

-36x^2-1x=0

a = -36; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-36)·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*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-36}=\frac{2}{-72}
=-1/36
$