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

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

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

We move all terms to the left:

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


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

2x(2x-4)

We multiply parentheses

4x^2-8x

Back to the equation:

-(4x^2-8x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+12x+8=0

a = -4; b = 12; c = +8;
Δ = b2-4ac
Δ = 122-4·(-4)·8
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{17}}{2*-4}=\frac{-12-4\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{17}}{2*-4}=\frac{-12+4\sqrt{17}}{-8}
$