(w+8)(w-5)=14

Solution for (w+8)(w-5)=14 equation:

(w+8)(w-5)=14

We move all terms to the left:

(w+8)(w-5)-(14)=0

We multiply parentheses ..

(+w^2-5w+8w-40)-14=0

We get rid of parentheses

w^2-5w+8w-40-14=0

We add all the numbers together, and all the variables

w^2+3w-54=0

a = 1; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·1·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*1}=\frac{-18}{2}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*1}=\frac{12}{2}
=6
$