[tex]\displaystyle\bf\\\frac{~~420^{(20}}{160}-\frac{1000}{x}+24\cdot7=180\\\\\frac{21}{8}-\frac{1000}{x}+168=180\\\\-\frac{1000}{x}=180-168-\frac{21}{8}\\\\-\frac{1000}{x}=12-\frac{21}{8}\\\\-\frac{1000}{x}=\frac{12\cdot8-21}{8}\\\\-\frac{1000}{x}=\frac{96-21}{8}\\\\-\frac{1000}{x}=\frac{75}{8}\\\\\x=\frac{-1000\cdot8}{75}=-\frac{40\cdot8}{3}\\\\ \boxed{\bf x=-\frac{320}{3}}[/tex]