Hey, I have experience marking the official Edexcel A-level exams. You are allowed to use the solver function to solve ANY basic quadratic equations as well as linear simultaneous equations. No marks are gained but showing the methods of solving (eg factorising, quad formula), but marks will be lost if you did it incorrectly manually, obviously haha.
But you cannot use the calculator for any equation with powers higher than 2 (eg cubic or quartic).
If a question states what you mentioned, usually they are looking for something specific algebraically, eg a method of proof, trig identities…etc.
perhaps if you could post the question out I would be able to answer your question better.
Hope this helps