The product of two consecutive positive integers is 27 more than 5 times the larger

X-smaller x+1-larger x(x+1)=5(x+1)+27 x^2+x=5x+5+27 x^2-4x=32 x^2-4x+4=32+4 (x-4)^2=36 x-4=6           X-4=-6 x=10            X=-2