SOLUTION: find the two possible values of p if p-3,3p+5 and 18p-5 are 3 consecutive terms of a GP

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Question 1107165: find the two possible values of p if p-3,3p+5 and 18p-5 are 3 consecutive terms of a GP
Answer by ikleyn(52788) About Me  (Show Source):
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Then the ratio of the third term to the second term is equal to the ratio of the second term to the first term,

since both ratios are equal to the common ratio, by the definition of the geometric progression:

%2818p-5%29%2F%283p%2B5%29 = %283p%2B5%29%2F%28p-3%29.

Cross-multiply to get

%2818p-5%29%2A%28p-3%29 = %283p%2B5%29%5E2.

It is the quadratic equation. Simplify it and reduce to the standard form.

Then find two roots of p using the quadratic formula.

After finding these values, restore the terms.