SOLUTION: consider two integers.The first number is three more than five times the second number.the difference of the squares of the 2 numbers is 45. Determine the two numbers

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Question 1181174: consider two integers.The first number is three more than five times the second number.the difference of the squares of the 2 numbers is 45. Determine the two numbers
Answer by greenestamps(13200) About Me  (Show Source):
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Let x be the second number; then the first number is 5x+3.

The difference between their squares is 45:

%285x%2B3%29%5E2-x%5E2=45
25x%5E2%2B30x%2B9-x%5E2=45
24x%5E2%2B30x-36=0
4x%5E2%2B5x-6=0
%284x-3%29%28x%2B2%29=0

x = 3/4 or x=-2; we want the integer solution.

ANSWER: x=-2; 5x+3=-7