Are you smarter than an 8th grader? #2

Number Theory Level 4

Given that $a$ has a remainder of $6$ and $b$ has a remainder of $1$ when divided by $14$ , what is the remainder of $x$ when divided by $14$ , given $x$ is an integer solution to $x^{2}-2ax+b=0$

This problem is part of the question set Mathematics in Anime. It appears in the anime Puella Magi Madoka Magica. Students attending the Math class are only $14$ years old, yet they are expected to solve this question on the spot!

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