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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(3(x-2)), so:

3(x-2)

We multiply parentheses

3x-6

Back to the equation:

-(3x-6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-5x+6=0

a = 1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*1}=\frac{6}{2}
=3
$