3x(2x-1)=(2x-1)

Solution for 3x(2x-1)=(2x-1) equation:

3x(2x-1)=(2x-1)

We move all terms to the left:

3x(2x-1)-((2x-1))=0

We multiply parentheses

6x^2-3x-((2x-1))=0


We calculate terms in parentheses: -((2x-1)), so:

(2x-1)

We get rid of parentheses

2x-1

Back to the equation:

-(2x-1)


We get rid of parentheses

6x^2-3x-2x+1=0

We add all the numbers together, and all the variables

6x^2-5x+1=0

a = 6; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·6·1
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*6}=\frac{4}{12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*6}=\frac{6}{12}
=1/2
$