use determinant
in form ax²+bx+c=0
when b²-4ac>0, it has 2 real roots
when b²-4ac=0, it has 1 real root
when b²-4ac<0, it has no real roots
so
we solve for no real roots
b²-4ac<0
a=3
c=7
b=-m
(-m)²-(4)(3)(7)<0
m²-84<0
add 84 both sides
m²<84
sqrt both sides
m<9.1 about
nearest integer
round down
m=9
answer is m=9