4(2a+8)a=-4

Solution for 4(2a+8)a=-4 equation:

4(2a+8)a=-4

We move all terms to the left:

4(2a+8)a-(-4)=0

We add all the numbers together, and all the variables

4(2a+8)a+4=0

We multiply parentheses

8a^2+32a+4=0

a = 8; b = 32; c = +4;
Δ = b2-4ac
Δ = 322-4·8·4
Δ = 896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{14}}{2*8}=\frac{-32-8\sqrt{14}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{14}}{2*8}=\frac{-32+8\sqrt{14}}{16}
$