Question 717596
Divide left and right members by 3.  Substitute for x^2 as a different single variable and solve for that variable; and then reverse the subsitution to continue solving for x.


Your equation is the same as {{{4x^4-x^2-18=0}}}.  


You could ignore the substitution for x^2 suggestion and go along with x^2 as the variable, and THEN continue on for x. The simpler equation on the left side is factorable, so you now have  {{{(4x^2-9)(x^2+2)=0}}}.


For x^2+2=0, no real solution.  Complex solution yes. No real one.  {{{i*sqrt(2)=x}}} or {{{-i*sqrt(2)}}}.


For 4x^2-9=0, 4x^2=9, x^2=9/4, {{{x=+3/2}}} or {{{x=-3/2}}}.