WoW When to use Slam

What the author is saying in the article you mentioned is, that he used basic arithmetic trasformations to get to the inequations below. If written as ratios it is more readable [substitution X for Avg. Weap Dam. and Y vor Waep Speed] i would recommend writing it down for clearity.

Operation used is written behind "|"

[X+140]*1/1.5 > [X+176]*1/Y |*1.5

<=> X+140 > [X+176]*1.5/Y

<=> X+140 > 1.5*X/Y + 264/Y | -1.5*X/Y

<=> X+140 - 1.5*X/Y > 264/Y | -140

<=> X - 1.5*X/Y > [264 - 140 Y]/Y

<=> (1 - 1,5/Y)*X > [264 - 140 Y]/Y

<=> X > [264 - 140 Y]/[Y*(1-1.5/Y)] = [264 - 140 Y]/[Y - 1.5*Y] = [264 - 140 Y]/[(1-1.5)*Y]

<=> X > [264 - 140 Y]/[-0.5*Y]

Now all he did to reach the 3rd equation is reintroduce that 264 = HS*1.5 and 140 = S for Heroic Strike's and Slam's bonus damage respectively. Leaving you with the desired equation.

And finally the author is saying that if your pair of Weap Speed and Avg Dmg fulfill this inequality you should use Slam instead of HS.

Feel free to ask for details.