(w+9)(w+4)=-6

Solution for (w+9)(w+4)=-6 equation:

(w+9)(w+4)=-6

We move all terms to the left:

(w+9)(w+4)-(-6)=0

We add all the numbers together, and all the variables

(w+9)(w+4)+6=0

We multiply parentheses ..

(+w^2+4w+9w+36)+6=0

We get rid of parentheses

w^2+4w+9w+36+6=0

We add all the numbers together, and all the variables

w^2+13w+42=0

a = 1; b = 13; c = +42;
Δ = b2-4ac
Δ = 132-4·1·42
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*1}=\frac{-14}{2}
=-7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*1}=\frac{-12}{2}
=-6
$