a(3a+16)=-16

Solution for a(3a+16)=-16 equation:

a(3a+16)=-16

We move all terms to the left:

a(3a+16)-(-16)=0

We add all the numbers together, and all the variables

a(3a+16)+16=0

We multiply parentheses

3a^2+16a+16=0

a = 3; b = 16; c = +16;
Δ = b2-4ac
Δ = 162-4·3·16
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8}{2*3}=\frac{-24}{6}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8}{2*3}=\frac{-8}{6}
=-1+1/3
$