3x(x-2)-4=2(x-1)-2

Solution for 3x(x-2)-4=2(x-1)-2 equation:

3x(x-2)-4=2(x-1)-2

We move all terms to the left:

3x(x-2)-4-(2(x-1)-2)=0

We multiply parentheses

3x^2-6x-(2(x-1)-2)-4=0


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

2(x-1)-2

We multiply parentheses

2x-2-2

We add all the numbers together, and all the variables

2x-4

Back to the equation:

-(2x-4)


We get rid of parentheses

3x^2-6x-2x+4-4=0

We add all the numbers together, and all the variables

3x^2-8x=0

a = 3; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·3·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*3}=\frac{16}{6}
=2+2/3
$