Before linear, quadratic, or cubic equations, there's one shared idea underneath all of them: finding the value that makes a statement true. This page is the starting point — pick a branch below once you've got the idea.
An equation is a mathematical statement that says two expressions are equal, joined by an "=" sign — for example, 2x + 3 = 11. It's a claim, not yet a fact: it's only true for certain values of the unknown (here, x).
A root (or solution) of an equation is any value of the unknown that makes the statement true when substituted in. For 2x + 3 = 11, substituting x = 4 gives 2(4) + 3 = 11, which checks out — so x = 4 is a root.
An equation can have one root, several roots, infinitely many, or none at all, depending on its shape. A big part of algebra is figuring out how many roots to expect and how to find them systematically, rather than by guessing.
Add 7 to both sides: 3x = 9. Divide both sides by 3: x = 3. Check: 3(3) − 7 = 2 ✓ — so x = 3 is the root.