3x(x+8)=-2

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

3x(x+8)=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x(x+8)+2=0

We multiply parentheses

3x^2+24x+2=0

a = 3; b = 24; c = +2;
Δ = b2-4ac
Δ = 242-4·3·2
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{138}}{2*3}=\frac{-24-2\sqrt{138}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{138}}{2*3}=\frac{-24+2\sqrt{138}}{6}
$