(a+9)(a+3)=-5

Solution for (a+9)(a+3)=-5 equation:

(a+9)(a+3)=-5

We move all terms to the left:

(a+9)(a+3)-(-5)=0

We add all the numbers together, and all the variables

(a+9)(a+3)+5=0

We multiply parentheses ..

(+a^2+3a+9a+27)+5=0

We get rid of parentheses

a^2+3a+9a+27+5=0

We add all the numbers together, and all the variables

a^2+12a+32=0

a = 1; b = 12; c = +32;
Δ = b2-4ac
Δ = 122-4·1·32
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4}{2*1}=\frac{-16}{2}
=-8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4}{2*1}=\frac{-8}{2}
=-4
$