(w-8)(w+4)=14

Solution for (w-8)(w+4)=14 equation:

(w-8)(w+4)=14

We move all terms to the left:

(w-8)(w+4)-(14)=0

We multiply parentheses ..

(+w^2+4w-8w-32)-14=0

We get rid of parentheses

w^2+4w-8w-32-14=0

We add all the numbers together, and all the variables

w^2-4w-46=0

a = 1; b = -4; c = -46;
Δ = b2-4ac
Δ = -42-4·1·(-46)
Δ = 200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10\sqrt{2}}{2*1}=\frac{4-10\sqrt{2}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10\sqrt{2}}{2*1}=\frac{4+10\sqrt{2}}{2}
$