7x(x-1)=x-1

Solution for 7x(x-1)=x-1 equation:

7x(x-1)=x-1

We move all terms to the left:

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

We multiply parentheses

7x^2-7x-(x-1)=0

We get rid of parentheses

7x^2-7x-x+1=0

We add all the numbers together, and all the variables

7x^2-8x+1=0

a = 7; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·7·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6}{2*7}=\frac{2}{14}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6}{2*7}=\frac{14}{14}
=1
$