x(x+4)+4(x+2)=2x+12

Solution for x(x+4)+4(x+2)=2x+12 equation:

x(x+4)+4(x+2)=2x+12

We move all terms to the left:

x(x+4)+4(x+2)-(2x+12)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+6x-4=0

a = 1; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·1·(-4)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{13}}{2*1}=\frac{-6-2\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{13}}{2*1}=\frac{-6+2\sqrt{13}}{2}
$