Use quadratic formula to find each root first.


α is the one with the + sign.

Find the cube of it and rewrite the right hand side in terms of α

There are many ways to do this question. Resubstitution into original equation works. I will demonstrate one later if I have time.

One way (and in fact, the easiest) is to factorise the terms in x by taking out x and then multiply both sides by the 'conjugate' of 2a - 3 i.e. 2a + 3.

2a2 - 3a = 7
a (2a - 3) = 7
a (2a - 3) (2a + 3) = 7 (2a + 3)
a (4a2 - 9) = 14a + 21
4a3 - 9a = 14a + 21
4a3 = 23a + 21

Thank you!