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

Apr 8, 2015

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

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

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

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