2x(x-3)=x-3

Solution for 2x(x-3)=x-3 equation:

2x(x-3)=x-3

We move all terms to the left:

2x(x-3)-(x-3)=0

We multiply parentheses

2x^2-6x-(x-3)=0

We get rid of parentheses

2x^2-6x-x+3=0

We add all the numbers together, and all the variables

2x^2-7x+3=0

a = 2; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·2·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*2}=\frac{2}{4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*2}=\frac{12}{4}
=3
$