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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

2(-1x+1)

We multiply parentheses

-2x+2

Back to the equation:

-(-2x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-1x-2=0

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