{{{9m^2=-2}}} Start with the given equation.



{{{9m^2+2=0}}} Get all terms to the left side.



Notice that the quadratic {{{9m^2+2}}} is in the form of {{{Am^2+Bm+C}}} where {{{A=9}}}, {{{B=0}}}, and {{{C=2}}}



Let's use the quadratic formula to solve for "m":



{{{m = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{m = (-(0) +- sqrt( (0)^2-4(9)(2) ))/(2(9))}}} Plug in  {{{A=9}}}, {{{B=0}}}, and {{{C=2}}}



{{{m = (0 +- sqrt( 0-4(9)(2) ))/(2(9))}}} Square {{{0}}} to get {{{0}}}. 



{{{m = (0 +- sqrt( 0-72 ))/(2(9))}}} Multiply {{{4(9)(2)}}} to get {{{72}}}



{{{m = (0 +- sqrt( -72 ))/(2(9))}}} Subtract {{{72}}} from {{{0}}} to get {{{-72}}}



{{{m = (0 +- sqrt( -72 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{m = (0 +- 6i*sqrt(2))/(18)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{m = (6i*sqrt(2))/(18)}}} or {{{m = -(6i*sqrt(2))/(18)}}} Break up the expression.  



{{{m = (1/3)*i*sqrt(2)}}} or {{{m = -(1/3)*i*sqrt(2)}}} Reduce



So the solutions are {{{m = (1/3)*i*sqrt(2)}}} or {{{m = -(1/3)*i*sqrt(2)}}}