7x(x-2)=x-2

Solution for 7x(x-2)=x-2 equation:

7x(x-2)=x-2

We move all terms to the left:

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

We multiply parentheses

7x^2-14x-(x-2)=0

We get rid of parentheses

7x^2-14x-x+2=0

We add all the numbers together, and all the variables

7x^2-15x+2=0

a = 7; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·7·2
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-13}{2*7}=\frac{2}{14}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+13}{2*7}=\frac{28}{14}
=2
$