What is the integer solution of $6x^2+9=21x$ ?

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Answer 1 · 2015-04-08T18:23:55

Re-arrange $6x^2+9 = 21x$
into the more usual form
$6x^2-21x+9 = 0$

then factor the left hand side
$(6x-3)(x-3)=0$

which implies
either $(6x-3)=0$ ...but this does not have an integer solution
or $(x-3) = 0$ ...which has an integer solution $x=3$

The only integer solution to $6x^2+9=21x$ is $x=3$

What is the integer solution of 6x^2+9=21x6x^2+9=21x?