book Maths Puzzle Numerical Ability

Why do you divide the sequence in the 2nd difference of a quadratic equation before adding it to your formula?

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Yikes nobody I know knows this stuff. Please Help
Thanks bunches.

2/3y + 4 = 2x

secondly


1/2(y + 5) + 4x = 3x
Hi Could you please help me to solve this problem:

Find a probability if a die is rolled 5 times: P(exactly one 5)