2x(4x+2)=4x-12(x-1)

Solution for 2x(4x+2)=4x-12(x-1) equation:

2x(4x+2)=4x-12(x-1)

We move all terms to the left:

2x(4x+2)-(4x-12(x-1))=0

We multiply parentheses

8x^2+4x-(4x-12(x-1))=0


We calculate terms in parentheses: -(4x-12(x-1)), so:

4x-12(x-1)

We multiply parentheses

4x-12x+12

We add all the numbers together, and all the variables

-8x+12

Back to the equation:

-(-8x+12)


We get rid of parentheses

8x^2+4x+8x-12=0

We add all the numbers together, and all the variables

8x^2+12x-12=0

a = 8; b = 12; c = -12;
Δ = b2-4ac
Δ = 122-4·8·(-12)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{33}}{2*8}=\frac{-12-4\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{33}}{2*8}=\frac{-12+4\sqrt{33}}{16}
$