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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(3x-4x(x-1)), so:

3x-4x(x-1)

We multiply parentheses

-4x^2+3x+4x

We add all the numbers together, and all the variables

-4x^2+7x

Back to the equation:

-(-4x^2+7x)


We add all the numbers together, and all the variables

-(-4x^2+7x)+x-4=0

We get rid of parentheses

4x^2-7x+x-4=0

We add all the numbers together, and all the variables

4x^2-6x-4=0

a = 4; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·4·(-4)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*4}=\frac{16}{8}
=2
$