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^2-4x+8=0

a = -4; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-4)·8
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*-4}=\frac{16}{-8}
=-2
$