(2x+6)(2x-6)=32x

Solution for (2x+6)(2x-6)=32x equation:

(2x+6)(2x-6)=32x

We move all terms to the left:

(2x+6)(2x-6)-(32x)=0

We add all the numbers together, and all the variables

-32x+(2x+6)(2x-6)=0

We use the square of the difference formula

4x^2-32x-36=0

a = 4; b = -32; c = -36;
Δ = b2-4ac
Δ = -322-4·4·(-36)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-40}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+40}{2*4}=\frac{72}{8}
=9
$