(w+17)(w+6)=0

Solution for (w+17)(w+6)=0 equation:

(w+17)(w+6)=0

We multiply parentheses ..

(+w^2+6w+17w+102)=0

We get rid of parentheses

w^2+6w+17w+102=0

We add all the numbers together, and all the variables

w^2+23w+102=0

a = 1; b = 23; c = +102;
Δ = b2-4ac
Δ = 232-4·1·102
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-11}{2*1}=\frac{-34}{2}
=-17
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+11}{2*1}=\frac{-12}{2}
=-6
$