Hello All, I'm attempting to understand the derivation of the cubic formula. I used the website, http://mathworld.wolfram.com/CubicFormula.html, to understand how the formula was originally derived, but I don't understand how to use the result for w. I'm referring to equation number 21 on the website. I know the other half of the page uses additional substitutions, but I'm trying to approach it one step at a time. I have done the substitutions by hand up to equation 21 as well and did try to use the results to solve a cubic equation, but didn't have any luck. My main problem was that the result for w is a quadratic formula, and I don't see how you can obtain 3 solutions from that equation. I tried to do it, but was only able to obtain two even after solving for w^3 and substituting all the way back to the starting equation before the first substitution. I've attached my work below. Could someone please help me understand how three solutions were obtained and why none of my substitutions worked? The equation I tried to solve is x^3 + 2x^2 - 5x - 6. I know rational root theorem or a plot will solve the problem, but I want to understand the equation as well.