Determine the value(s) of m so that the quadratic equation mx2+6x = −m has no real roots. (i.e. no solution)

Answer 1

Let's arrange it into the normal appearance of a quadratic
mx^2 + 6x + m = 0

to have no real roots, the discriminant < 0
b^2 - 4ac < 0
36 - 4(m)(m) < 0
4m^2 > 36
m^2 > 9
± m > 3
m > 3 OR m < -3

Answer 2

adding m ... m x^2 + 6x + m = 0

the discriminant ... b^2 - 4 a c ... is negative for no real roots

in this case ... 36 - 4 m^2 < 0 ... - 4 m^2 < -36 ... 4 m^2 > 36 ... m^2 > 9

-3 > m ... or ... m > 3