(w-8)(w+9)=72

Solution for (w-8)(w+9)=72 equation:

(w-8)(w+9)=72

We move all terms to the left:

(w-8)(w+9)-(72)=0

We multiply parentheses ..

(+w^2+9w-8w-72)-72=0

We get rid of parentheses

w^2+9w-8w-72-72=0

We add all the numbers together, and all the variables

w^2+w-144=0

a = 1; b = 1; c = -144;
Δ = b2-4ac
Δ = 12-4·1·(-144)
Δ = 577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{577}}{2*1}=\frac{-1-\sqrt{577}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{577}}{2*1}=\frac{-1+\sqrt{577}}{2}
$