(w-18)(w+2)=1152

Solution for (w-18)(w+2)=1152 equation:

(w-18)(w+2)=1152

We move all terms to the left:

(w-18)(w+2)-(1152)=0

We multiply parentheses ..

(+w^2+2w-18w-36)-1152=0

We get rid of parentheses

w^2+2w-18w-36-1152=0

We add all the numbers together, and all the variables

w^2-16w-1188=0

a = 1; b = -16; c = -1188;
Δ = b2-4ac
Δ = -162-4·1·(-1188)
Δ = 5008
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:

$\sqrt{\Delta}=\sqrt{5008}=\sqrt{16*313}=\sqrt{16}*\sqrt{313}=4\sqrt{313}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{313}}{2*1}=\frac{16-4\sqrt{313}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{313}}{2*1}=\frac{16+4\sqrt{313}}{2}
$