Depth

What you have been given is an equation with a single unknown. It should be solvable for x without any additional information.

There seems to be missing information. Most corks float, for example. The depth of the cork remaining underwater would partly be a function of its specific gravity. I don't see that mentioned.

Equation works for x = 3.1. But I don't know what that means

That is the complete problem. Please explain how you obtained the answer. Thanks.

the cubic polynomial

2x^3-6x^2+1.92=0

has three real roots

x= 2.884630546095557;
x= -0.522078827044294;
and
x= 0.6374482809487371

Online cubic polynomial solver

Rap

Thanks raprap.

Randy, what are you doing?

I ran across some old algebra problems from the early 1900's. I thought they were interesting and did not know how to solve them. I wanted to see the solutions and was asking for assistance.

How does the equation apply to the cork?

The equation was specified in the problem.