What are the solutionso of 8x^2 = 6 + 22x

You can get all the terms on one side, and then solve for x by any means:


Factor out a -2:


Factor this equation:


I will use the AC method. To use it, first multiply a and c (in ax^2 + bx +c):


Now, look for two numbers that multiply to -12 and add to -11. Obviously these numbers are -12 and 1. (-12*1 = -12 and -12+1  = -11). Now, because of rules, you set it up in a Punnett square:

4x^2        -12x
x              -3

Now, we find common factors of the terms in rows:
     _x_______-3__
4x| 4x^2        -12x
1   | x              -3

So, you can use this to write an equivalent expression to the quadratic given:


Now, we known the factors are (solve for x): 3 and -1/4.