Answer:
x =(22-√196)/6=(11-7)/3= 1.333
Step-by-step explanation:
(3x2 -  22x) +  24  = 0 
The first term is,  3x2  its coefficient is  3 .
The middle term is,  -22x  its coefficient is  -22 .
The last term, "the constant", is  +24 
Step-1 : Multiply the coefficient of the first term by the constant   3 • 24 = 72 
Step-2 : Find two factors of  72  whose sum equals the coefficient of the middle term, which is   -22 .
      -72    +    -1    =    -73	
      -36    +    -2    =    -38	
      -24    +    -3    =    -27	
      -18    +    -4    =    -22    That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  -4 
                     3x2 - 18x - 4x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
                    3x • (x-6)
              Add up the last 2 terms, pulling out common factors :
                    4 • (x-6)
Step-5 : Add up the four terms of step 4 :
                    (3x-4)  •  (x-6)
             Which is the desired factorization
Equation at the end of step 2:
  (x - 6) • (3x - 4)  = 0 
STEP 3:
Theory - Roots of a product
 3.1    A product of several terms equals zero. 
 When a product of two or more terms equals zero, then at least one of the terms must be zero. 
 We shall now solve each term = 0 separately 
 In other words, we are going to solve as many equations as there are terms in the product 
 Any solution of term = 0 solves product = 0 as well.