(4x)(x-2)=256^2

Solution for (4x)(x-2)=256^2 equation:

(4x)(x-2)=256^2

We move all terms to the left:

(4x)(x-2)-(256^2)=0

We add all the numbers together, and all the variables

4x(x-2)-65536=0

We multiply parentheses

4x^2-8x-65536=0

a = 4; b = -8; c = -65536;
Δ = b2-4ac
Δ = -82-4·4·(-65536)
Δ = 1048640
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:

$\sqrt{\Delta}=\sqrt{1048640}=\sqrt{64*16385}=\sqrt{64}*\sqrt{16385}=8\sqrt{16385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{16385}}{2*4}=\frac{8-8\sqrt{16385}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{16385}}{2*4}=\frac{8+8\sqrt{16385}}{8}
$