12x-8(x+1)(x-1)-8x(x-1)=14x-5+(4x-2)(4x+2)

Solution for 12x-8(x+1)(x-1)-8x(x-1)=14x-5+(4x-2)(4x+2) equation:

12x-8(x+1)(x-1)-8x(x-1)=14x-5+(4x-2)(4x+2)

We move all terms to the left:

12x-8(x+1)(x-1)-8x(x-1)-(14x-5+(4x-2)(4x+2))=0

We use the square of the difference formula

x^2+16x^2+12x-8x(x-1)+1+4=0

We multiply parentheses

x^2+16x^2-8x^2+12x+8x+1+4=0

We add all the numbers together, and all the variables

9x^2+20x+5=0

a = 9; b = 20; c = +5;
Δ = b2-4ac
Δ = 202-4·9·5
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{55}}{2*9}=\frac{-20-2\sqrt{55}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{55}}{2*9}=\frac{-20+2\sqrt{55}}{18}
$