W(w-2)(w-3)=50

Solution for W(w-2)(w-3)=50 equation:

(W-2)(W-3)=50

We move all terms to the left:

(W-2)(W-3)-(50)=0

We multiply parentheses ..

(+W^2-3W-2W+6)-50=0

We get rid of parentheses

W^2-3W-2W+6-50=0

We add all the numbers together, and all the variables

W^2-5W-44=0

a = 1; b = -5; c = -44;
Δ = b2-4ac
Δ = -52-4·1·(-44)
Δ = 201
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{-(-5)-\sqrt{201}}{2*1}=\frac{5-\sqrt{201}}{2}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{201}}{2*1}=\frac{5+\sqrt{201}}{2}
$