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

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

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

We move all terms to the left:

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

We multiply parentheses

-8x^2+16x-(2(2x-1))=0


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

2(2x-1)

We multiply parentheses

4x-2

Back to the equation:

-(4x-2)


We get rid of parentheses

-8x^2+16x-4x+2=0

We add all the numbers together, and all the variables

-8x^2+12x+2=0

a = -8; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-8)·2
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{13}}{2*-8}=\frac{-12-4\sqrt{13}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{13}}{2*-8}=\frac{-12+4\sqrt{13}}{-16}
$