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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We use the square of the difference formula

4x^2-1x-16=0

a = 4; b = -1; c = -16;
Δ = b2-4ac
Δ = -12-4·4·(-16)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{257}}{2*4}=\frac{1-\sqrt{257}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{257}}{2*4}=\frac{1+\sqrt{257}}{8}
$