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

Solution for (2x-1)2=4x(x-2) equation:

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

We move all terms to the left:

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

We multiply parentheses

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


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

4x(x-2)

We multiply parentheses

4x^2-8x

Back to the equation:

-(4x^2-8x)


We get rid of parentheses

-4x^2+4x+8x-2=0

We add all the numbers together, and all the variables

-4x^2+12x-2=0

a = -4; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·(-4)·(-2)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{7}}{2*-4}=\frac{-12-4\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{7}}{2*-4}=\frac{-12+4\sqrt{7}}{-8}
$