what does solution of an equation mean in math
Equation solving In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign. When seeking a solution, one or more free variables are designated as unknowns. A solution is an assignment of expressions to the unknown variables that makes the equality in the equation true. In other words, a solution is an expression or a collection of expressions (one for each unknown) such that, when substituted for the unknowns, the equation becomes an identity. A problem of solving an equation may be numeric or symbolic. Solving an equation numerically means that only numbers represented explicitly as numerals (not as an expression involving variables), are admitted as solutions. Solving an equation symbolically means that expressions that may contain known variables or possibly also variables not in the original equation are admitted as solutions.
Quadratic equation A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.
Exponentiation Any nonzero number raised to the 0 power is 1:[11]
Algorithm As an effective method, an algorithm can be expressed within a finite amount of space and time[1] and in a well-defined formal language[2] for calculating a function.[3] Starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, proceeds through a finite[5] number of well-defined successive states, eventually producing "output"[6] and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.[7]