-2x(x+4)=6x+24

Solution for -2x(x+4)=6x+24 equation:

-2x(x+4)=6x+24

We move all terms to the left:

-2x(x+4)-(6x+24)=0

We multiply parentheses

-2x^2-8x-(6x+24)=0

We get rid of parentheses

-2x^2-8x-6x-24=0

We add all the numbers together, and all the variables

-2x^2-14x-24=0

a = -2; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·(-2)·(-24)
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*-2}=\frac{12}{-4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*-2}=\frac{16}{-4}
=-4
$