The work concerns nondegenerate first-order quasilinear partial differential equations with one unknown function and two independent variables. An example of such an equation that has an everywhere dense multivalued solution is constructed. This construction is an explicit and constructive one. Namely, all the coefficients of the equation are explicit combinations of standard algebraic functions in a domain of the three-dimensional Euclidean space (one dependent and two independent variables). Furthermore, all the terms of the multivalued solution are also explicit combinations of standard algebraic and trigonometric functions.