W(w-1)(w-2)=6

Solution for W(w-1)(w-2)=6 equation:

(W-1)(W-2)=6

We move all terms to the left:

(W-1)(W-2)-(6)=0

We multiply parentheses ..

(+W^2-2W-1W+2)-6=0

We get rid of parentheses

W^2-2W-1W+2-6=0

We add all the numbers together, and all the variables

W^2-3W-4=0

a = 1; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·1·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*1}=\frac{-2}{2}
=-1
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*1}=\frac{8}{2}
=4
$