Calvin visits a Planet called Pandora!

Number Theory Level 3

Calvin went to a newly discovered planet called "Pandora" to research their advancements in the field of Mathematics. He found the following equation scrawled in the dust:

\[\large{3x^2 - 25x + 66 = 0 \quad \Longrightarrow \quad x=4 \text{ or } x=9}\]

Can you help Calvin in finding the base, which is used in the Number System on Pandora?

Note: Symbols for digits in the Pandora System and Decimal system have the same value. e.g. 6 in Pandora represents six.


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