2x+4=2x(2x+3)

Solution for 2x+4=2x(2x+3) equation:

2x+4=2x(2x+3)

We move all terms to the left:

2x+4-(2x(2x+3))=0


We calculate terms in parentheses: -(2x(2x+3)), so:

2x(2x+3)

We multiply parentheses

4x^2+6x

Back to the equation:

-(4x^2+6x)


We get rid of parentheses

-4x^2+2x-6x+4=0

We add all the numbers together, and all the variables

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

a = -4; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-4)·4
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{-(-4)-4\sqrt{5}}{2*-4}=\frac{4-4\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*-4}=\frac{4+4\sqrt{5}}{-8}
$