What is the solution set of 2x^2+x=15○3,-5/2○-3,5/2○2,-3/2

Rewrite 2x^2+x=15 as 2x^2+ x - 15 = 0.  Use your favorite method to solve this for x.  I prefer synthetic div., so will check out whether or not 2 is a root:

     
2  /   2     1     -15
               4      10
   
       2      5      -5   Since there is a non-zero remainder, 2 is NOT a root.  Eliminate the 3rd answer choice.

Try -3.  If used as a divisor in synth. div., will the remainder be zero or not zero?  If zero, then -3 is a solution / root.  

And so on.