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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

4x(x-1)

We multiply parentheses

4x^2-4x

Back to the equation:

-(4x^2-4x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-4)·6
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*-4}=\frac{-6-2\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*-4}=\frac{-6+2\sqrt{33}}{-8}
$