Question 81791
m^2 + 81 = -18m

Move everything to one side: m^2 + 18 m + 81

= (m + 9)(m + 9) <-- This is a quadratic equation.

m = -9 

This solution is called a double root or a root of multiplicity 2. 

You also posted another quadratic equation, try that one yourself from this example.