Love & Marriage

Algebra Level 1

A mathematician decided to stay married to his wife for as long as she (cumulatively) complimented him more often than she nagged him. Once the cumulative nagging caught up with the cumulative compliments, he would divorce her.

If \( N \) is the number of years since the wedding, he determined that the cumulative number of compliments was \( 40N \), while the cumulative amount of nagging was \( 2N^{2} \). Assuming he stayed true to his word, for how many years did he stay married to his wife?

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