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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

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


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

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

We multiply parentheses

-12x^2+6x+4x-2

We add all the numbers together, and all the variables

-12x^2+10x-2

Back to the equation:

-(-12x^2+10x-2)


We get rid of parentheses

12x^2-10x+4x+2-4=0

We add all the numbers together, and all the variables

12x^2-6x-2=0

a = 12; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·12·(-2)
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{33}}{2*12}=\frac{6-2\sqrt{33}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{33}}{2*12}=\frac{6+2\sqrt{33}}{24}
$