8x-2=2x(4x-2)

Solution for 8x-2=2x(4x-2) equation:

8x-2=2x(4x-2)

We move all terms to the left:

8x-2-(2x(4x-2))=0


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

2x(4x-2)

We multiply parentheses

8x^2-4x

Back to the equation:

-(8x^2-4x)


We get rid of parentheses

-8x^2+8x+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 = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{5}}{2*-8}=\frac{-12-4\sqrt{5}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{5}}{2*-8}=\frac{-12+4\sqrt{5}}{-16}
$