How do you solve #15x^2-11x-3=0#?
I always solve quadratic equations the same way. Spend 2 to 3 minutes trying to factor using integers or square root method, then use the quadratics formula.
The "somethings have to be
None of the other appear to work, so check the disciminant (some people do this first).
The discriminant is positive so there are 2 real solutions, but it is not a perfect square, so the solutions are not rational.