równaniu

Równaniu is a form of the Polish noun równanie. It is the locative (and, in some descriptions, the dative) singular form, used when referring to an equation in a sentence, for example in w równaniu x + 2 = 5 or o równaniu.

In mathematics, an equation is a statement that expresses the equality of two expressions. It involves unknowns to be determined and states that the two sides have the same value for certain values of those unknowns. Equations can be simple or very complex and may describe relationships between quantities, functions, or variables.

Common types of equations include równania liniowe (linear equations), równania kwadratowe (quadratic equations), and równania wielomianowe (polynomial equations). There are also równania różniczkowe (differential equations) in which a function and its derivatives are related. Solving an equation means finding the values of the unknowns that satisfy the equality. Methods vary by type and can include algebraic manipulation, factoring, applying the quadratic formula, substitution, elimination, or, for systems of equations, matrix techniques.

Beyond mathematics, równanie appears in Polish grammar as a noun. The form równaniu represents the locative/dative singular, used with certain prepositions or verbs. Other case forms include równanie (nominative), równania (genitive), and równaniem (instrumental). The term is commonly encountered in both mathematical discourse and linguistic description.