设两根为x1,x2.
则x1+x2=-(m+9)
x1×x2=2m+6
由题意知x1^2+x2^2=24
得,(x1+x2)^2-2×x1×x2=24
则,[-(m+9)]^2-2×(2m+6)=24
解得:m^2+18m+81-4m-12-24=0
m^2+14m+45=0
m1=-5,m2=-9