An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an 'equals' sign. For example: This equation states that 12 is equal to the sum of 7 and 5, which is obviously true. In an equation, the left side is always equal to the right side.
The most common equations contain one or more variables. If we let x stand for an unknown number, and write the equation We know the left side and right side are equal, so we can see that x must be 12+5 or 17. This is the only value that x can have that makes the equation a true statement. We say that x=17 'satisfies' the equation.
This process of finding the value of the unknowns is called "solving the equation". We often say that we "solve for x" - meaning solve the equation to find the value of the unknown number x.
You will often see things that are called equations when they are not. For example you may see something like this referred to as an equation: It does not have an equals sign in it, and so is not an equation. It is called an 'expression'.
The study of algebra is in large part about learning ways to solve various kinds equations. For example, there are ways to solve quadratic equations such as