Finding roots of complex numbers

The question:

i) Find the complex square roots of -24-10i by solving for x, y real.

ii) Hence, find the roots of the quadratic in "a+ib" form where a, b are real numbers.

My attempt:

i) I got the answer

ii) This is where I have trouble. The question appears to suggest that I use the result of part i) to solve part ii). I'm not sure how they relate. I was thinking of using the quadratic formula, but perhaps there's a quicker way?

Any assistance would be greatly appreciated!