We can get an approximate value for x by ignoring the rounding steps temporarily.

5*4*3*x^3 ~ 273

x^3 ~ 4.55

x ~ 1.657…

We know that the round(4x(round(3x)) part has been rounded to an integer, so to try to discover exactly what integer it is we can plug our approximate value of x to the outside of it:

5(1.657)(integer) ~ 273

integer ~ 273/(5(1.657)) ~ 32.95

This is close to an integer, 33, but we need to test it by plugging it back in:

Assume the value of round(4x(round(3x)) is indeed 33:

5x*33=273

x = 273/(5*33) = 273/165 = 91/55

Plugging that value into round(4x(round(3x)) indeed gives 33, so this is the correct answer.

x = 91/55 = 1.6545454..

Since this is a strictly increasing function (except where 3x rounds to zero), once we have found an answer, we can be sure it is the only answer.