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

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

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

We move all terms to the left:

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

We multiply parentheses

3x-(x+x(x+2))+12=0


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

x+x(x+2)

We multiply parentheses

x^2+x+2x

We add all the numbers together, and all the variables

x^2+3x

Back to the equation:

-(x^2+3x)


We get rid of parentheses

-x^2+3x-3x+12=0

We add all the numbers together, and all the variables

-1x^2+12=0

a = -1; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-1)·12
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-1}=\frac{0-4\sqrt{3}}{-2}
=-\frac{4\sqrt{3}}{-2}
=-\frac{2\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-1}=\frac{0+4\sqrt{3}}{-2}
=\frac{4\sqrt{3}}{-2}
=\frac{2\sqrt{3}}{-1}
$