\(\displaystyle G(x) \ = \ 24x^2-24, \ H(x) \ = \ 55x\)
\(\displaystyle G(x) \ > \ H(x) \ \implies \ 24x^2-24 \ > \ 55x, \ \implies \ 24x^2-55x-24 \ > \ 0, \ (3x-8)(8x+3) \ > \ 0.\)
\(\displaystyle Now, \ inequalities \ are \ a \ little \ tricky, \ so \ let \ 3x-8 \ = \ 0, \ implies \ x \ = \ 8/3 \ and\)
\(\displaystyle let \ 8x+3 \ = \ 0, \ \implies \ x \ = \ -3/8.\)
\(\displaystyle --------------0+++++++++++++++++++++++++++++++++++++\)
\(\displaystyle --------------------------------0++++++++++++++++++++++++\)
\(\displaystyle Hence \ x \ < \ -3/8 \ and \ x \ >8/3 \ or \ (-\infty,-3/8)U(8/3,\infty)\)