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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -((x-2)), so:

(x-2)

We get rid of parentheses

x-2

Back to the equation:

-(x-2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-7x+2=0

a = 3; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·3·2
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*3}=\frac{2}{6}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*3}=\frac{12}{6}
=2
$