2x-2=3x(x-1)-5(6-2x)

Solution for 2x-2=3x(x-1)-5(6-2x) equation:

2x-2=3x(x-1)-5(6-2x)

We move all terms to the left:

2x-2-(3x(x-1)-5(6-2x))=0

We add all the numbers together, and all the variables

2x-(3x(x-1)-5(-2x+6))-2=0


We calculate terms in parentheses: -(3x(x-1)-5(-2x+6)), so:

3x(x-1)-5(-2x+6)

We multiply parentheses

3x^2-3x+10x-30

We add all the numbers together, and all the variables

3x^2+7x-30

Back to the equation:

-(3x^2+7x-30)


We get rid of parentheses

-3x^2+2x-7x+30-2=0

We add all the numbers together, and all the variables

-3x^2-5x+28=0

a = -3; b = -5; c = +28;
Δ = b2-4ac
Δ = -52-4·(-3)·28
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*-3}=\frac{24}{-6}
=-4
$