256=(x-2)(2x-1)

Solution for 256=(x-2)(2x-1) equation:

256=(x-2)(2x-1)

We move all terms to the left:

256-((x-2)(2x-1))=0

We multiply parentheses ..

-((+2x^2-1x-4x+2))+256=0


We calculate terms in parentheses: -((+2x^2-1x-4x+2)), so:

(+2x^2-1x-4x+2)

We get rid of parentheses

2x^2-1x-4x+2

We add all the numbers together, and all the variables

2x^2-5x+2

Back to the equation:

-(2x^2-5x+2)


We get rid of parentheses

-2x^2+5x-2+256=0

We add all the numbers together, and all the variables

-2x^2+5x+254=0

a = -2; b = 5; c = +254;
Δ = b2-4ac
Δ = 52-4·(-2)·254
Δ = 2057
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:

$\sqrt{\Delta}=\sqrt{2057}=\sqrt{121*17}=\sqrt{121}*\sqrt{17}=11\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11\sqrt{17}}{2*-2}=\frac{-5-11\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11\sqrt{17}}{2*-2}=\frac{-5+11\sqrt{17}}{-4}
$