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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-4x^2+20x+4=0

a = -4; b = 20; c = +4;
Δ = b2-4ac
Δ = 202-4·(-4)·4
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{29}}{2*-4}=\frac{-20-4\sqrt{29}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{29}}{2*-4}=\frac{-20+4\sqrt{29}}{-8}
$