(s+9)(s+2)=-6

Solution for (s+9)(s+2)=-6 equation:

(s+9)(s+2)=-6

We move all terms to the left:

(s+9)(s+2)-(-6)=0

We add all the numbers together, and all the variables

(s+9)(s+2)+6=0

We multiply parentheses ..

(+s^2+2s+9s+18)+6=0

We get rid of parentheses

s^2+2s+9s+18+6=0

We add all the numbers together, and all the variables

s^2+11s+24=0

a = 1; b = 11; c = +24;
Δ = b2-4ac
Δ = 112-4·1·24
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*1}=\frac{-16}{2}
=-8
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*1}=\frac{-6}{2}
=-3
$