4x(x+8)=-24

Solution for 4x(x+8)=-24 equation:

4x(x+8)=-24

We move all terms to the left:

4x(x+8)-(-24)=0

We add all the numbers together, and all the variables

4x(x+8)+24=0

We multiply parentheses

4x^2+32x+24=0

a = 4; b = 32; c = +24;
Δ = b2-4ac
Δ = 322-4·4·24
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{10}}{2*4}=\frac{-32-8\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{10}}{2*4}=\frac{-32+8\sqrt{10}}{8}
$