4x(x-2)=x-2

Solution for 4x(x-2)=x-2 equation:

4x(x-2)=x-2

We move all terms to the left:

4x(x-2)-(x-2)=0

We multiply parentheses

4x^2-8x-(x-2)=0

We get rid of parentheses

4x^2-8x-x+2=0

We add all the numbers together, and all the variables

4x^2-9x+2=0

a = 4; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·4·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*4}=\frac{16}{8}
=2
$