Δ=(3N+2)^2-4(3N^2-74)=-3N^2+12N+300≥0
即
N^2-4N-100≤0
∴2(1-√26)≤N≤2(1+√26)
又∵N∈Z
∴-8≤N≤12
∴所有实根之和
S=∑(1/2(3N+2+√∆)+1/2(3N+2-√∆)) -8≤N≤12,N∈Z
=∑(3N+2) -8≤N≤12,N∈Z
=168