(w-8)(2w-1)=180

Solution for (w-8)(2w-1)=180 equation:

(w-8)(2w-1)=180

We move all terms to the left:

(w-8)(2w-1)-(180)=0

We multiply parentheses ..

(+2w^2-1w-16w+8)-180=0

We get rid of parentheses

2w^2-1w-16w+8-180=0

We add all the numbers together, and all the variables

2w^2-17w-172=0

a = 2; b = -17; c = -172;
Δ = b2-4ac
Δ = -172-4·2·(-172)
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{185}}{2*2}=\frac{17-3\sqrt{185}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{185}}{2*2}=\frac{17+3\sqrt{185}}{4}
$