-4x(x+2)=6x+12

Solution for -4x(x+2)=6x+12 equation:

-4x(x+2)=6x+12

We move all terms to the left:

-4x(x+2)-(6x+12)=0

We multiply parentheses

-4x^2-8x-(6x+12)=0

We get rid of parentheses

-4x^2-8x-6x-12=0

We add all the numbers together, and all the variables

-4x^2-14x-12=0

a = -4; b = -14; c = -12;
Δ = b2-4ac
Δ = -142-4·(-4)·(-12)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2}{2*-4}=\frac{12}{-8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*-4}=\frac{16}{-8}
=-2
$