5x(x-1)=x-1

Solution for 5x(x-1)=x-1 equation:

5x(x-1)=x-1

We move all terms to the left:

5x(x-1)-(x-1)=0

We multiply parentheses

5x^2-5x-(x-1)=0

We get rid of parentheses

5x^2-5x-x+1=0

We add all the numbers together, and all the variables

5x^2-6x+1=0

a = 5; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·5·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*5}=\frac{2}{10}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*5}=\frac{10}{10}
=1
$