Let the integral root be γ. ‌⇒‌‌6γ3−25γ2+2γ+8=0 ‌⇒‌‌6γ3−24γ2−γ2+2γ+8=0 ‌⇒‌‌6γ2(γ−4)−(γ2−2γ−8)=0 ‌⇒‌‌6γ2(γ−4)−(γ−4)(γ+2)=0 ‌⇒‌‌(γ−4)(6γ2−γ−2)=0 ‌⇒‌‌(γ−4)(6γ2+3γ−4γ−2)=0 ‌⇒‌‌(γ−4)(3γ(2γ+1))−2(2γ+1))=0 ‌⇒‌‌γ=4,β=‌
