Question 9228
 You should type the equation as 3x^2 -(p-4)x-(2p+1)=0 

 which is equivalent to x^2 -(p-4)/3 x-(2p+1)/3=0 
 since alpha ,beta are two roots,from the relationship of roots and
 coeffieicnts,we have 
 
 alpha + beta = (p-4)/3   and
 alpha * beta =  -(2p+1)/3

 to find the required equation, we have to get the
 sum and product of  alpha+ 2 and beta + 2
 
 Now, alpha+ 2 + beta + 2  = (p-4)/3 + 4 = (p+8)/3  
  and their product as
 (alpha+ 2)  * (beta + 2  ) 
 = alpha  * beta  + 2(alpha + beta )+ 4 
 =  -(2p+1)/3 + 2(p-4)/3 + 4
 = -9/3 + 4
 = 1

 So,the solution equation is

 x^2 -(p+8)/3 x + 1 = 0 
or equivalently
 3x^2 -(p+8) x + 3 = 0 
 
 If you have trouble understanding the details, try to think carefully.
 I may not supply further explanations.

 Kenny