Note that . That is, that in the general form , b is the sum of the roots and c is their product.
To get the second equation, into that form I would first divide through by 2: with b= -3a/2, c= -9/2. The first equation, has b= -4a and c= 3.
If we call the common root, "B" and the other roots "A" and "C", we must have A+ B= -3a/2, B+ C= -4a, AB= -9/2, and BC= 3. That gives four equations to solve for the four unknowns, A, B, C, and a. From AB= -9/2, for example, A= -9/(2B) and from BC= 3, C= 3/B. Putting those into A+ B= -3a/2, and B+ C= -4a, -9/(2B)+ B= -3a/2 and B+ 3/B= -4a so you are now reduced to two equations in B and a.