3x(x+8)=-16-2x

Solution for 3x(x+8)=-16-2x equation:

3x(x+8)=-16-2x

We move all terms to the left:

3x(x+8)-(-16-2x)=0

We add all the numbers together, and all the variables

3x(x+8)-(-2x-16)=0

We multiply parentheses

3x^2+24x-(-2x-16)=0

We get rid of parentheses

3x^2+24x+2x+16=0

We add all the numbers together, and all the variables

3x^2+26x+16=0

a = 3; b = 26; c = +16;
Δ = b2-4ac
Δ = 262-4·3·16
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-22}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+22}{2*3}=\frac{-4}{6}
=-2/3
$