exam Maths Puzzle Numerical Ability

graph
2x-y=5

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exam Other Question

Given the quadratic equation x^2-15=2k(x-4),find k if there are two real and equal roots. I got k=5 and k=3 but I would appreciate it if someone could explain it in detail to me :) Thanks. Multiply and collect terms

(x-4)(2x^+4)+(x+4)(x^3-1)-x^2-x-1)