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How can I solve quadratic equations using modular arithmetic? E.g.

$$2x^2 + 8x + 2 = 0 \pmod{23}$$

N.b. I have changed the figures from those in my homework question because I don't want a solution I want to understand the process. Consequently the example I gave might not have solutions. For the example I am working from divide the LHS by 2.

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    I like that you changed the question so as not to accidentally solve your homework. But note that 2 is a unit mod 23, so in fact you can legally divide both sides by 2, so this problem is essentially identical to the original one.2012-12-19
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    @AaronMazel-Gee Who would have thought that coming up with examples could be difficult :/2012-12-19

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