(w+5)(w+7)=15

Solution for (w+5)(w+7)=15 equation:

(w+5)(w+7)=15

We move all terms to the left:

(w+5)(w+7)-(15)=0

We multiply parentheses ..

(+w^2+7w+5w+35)-15=0

We get rid of parentheses

w^2+7w+5w+35-15=0

We add all the numbers together, and all the variables

w^2+12w+20=0

a = 1; b = 12; c = +20;
Δ = b2-4ac
Δ = 122-4·1·20
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*1}=\frac{-20}{2}
=-10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*1}=\frac{-4}{2}
=-2
$