3x2-2x-1=2(x-1)

Solution for 3x2-2x-1=2(x-1) equation:

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

We move all terms to the left:

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


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

2(x-1)

We multiply parentheses

2x-2

Back to the equation:

-(2x-2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-4x+1=0

a = 3; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·3·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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