I don't think your work is correct. If I am reading your post correctly, you have assumed that x[sup:1nhq8wwl]2[/sup:1nhq8wwl] is the same as 2x. That is not the case. x[sup:1nhq8wwl]2[/sup:1nhq8wwl] - 6x is not the same as 2x - 6x. My suggestion is to get all the terms on the left side of the equation, then see if you can solve for x by factoring. You can check your answer by plugging it back in to your original equation to see if it tells the truth.
6x - 8 = x[sup:1nhq8wwl]2[/sup:1nhq8wwl]
If x = 0.5 then we have
6(0.5) - 8 = (0.5)[sup:1nhq8wwl]2[/sup:1nhq8wwl]
3 - 8 = 0.25 which is not true. Therefore x is not equal to 0.5.
