0=7x-7/x-1

Solution for 0=7x-7/x-1 equation:

0=7x-7/x-1

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-7x+7/x+1=0

We multiply all the terms by the denominator


-7x*x+1*x+7=0

We add all the numbers together, and all the variables

x-7x*x+7=0

Wy multiply elements

-7x^2+x+7=0

a = -7; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-7)·7
Δ = 197
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{197}}{2*-7}=\frac{-1-\sqrt{197}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{197}}{2*-7}=\frac{-1+\sqrt{197}}{-14}
$