Question 859644
Let n = the integer
The problem statement gives us
(1) 3 + 2*n^2 = 7*n or
(2) 2*n^2 - 7*n + 3 = 0 which factors to
(3) (2n - 1)*(n - 3) = 0
Set each factor equal to zero and solve for n gives us
(4) n = 1/2,3
Since n is an integer we select
(5) n = 3
Check this with (1).
Is (3 + 2*3^2 = 7*3)?
Is (3 + 2*9 = 21)?
Is (3 + 18 = 21)?
Is (21 = 21)? Yes
Answer: The integer is 3.