Draw a graph of the function and observe where the graph cuts the x axis: near -2.4, -0.44, 2.84. These are approximate solutions. To find more accurate solutions requires the use of a calculator and an iterative process. One iterative process: x=(x^3-3)/7. Starting with x=0, compute -3/7 as the first approximate solution, then feed this value back into the right-hand expression: -1056/2401; -0.440725...; -0.440800...; -0.440807...; ...; -0.4408077115... The other approximate solutions diverge, so this iterative process doesn't work.
Try a different iterative process:
x=cuberoot(7x+3); start with x=2.84: ..., 2.838469253. Start with -2.4: -2.397661541.
The answer is irrational: x=-2.3977, -0.4408, 2.8385 approx.