---
title: "Quadratic Formula Calculator — Solve ax²+bx+c=0"
description: "Solve any quadratic equation. Enter a, b, c to get discriminant, real or complex roots, vertex, and axis of symmetry. Free calculator with full working."
url: "https://worldcalculators.org/calculators/quadratic-formula/"
canonical: "https://worldcalculators.org/calculators/quadratic-formula/"
---

# Quadratic Formula Calculator

Solve any quadratic equation. Enter a, b, c to get discriminant, real or complex roots, vertex, and axis of symmetry. Free calculator with full working.

## Quick answer

x = (−b ± √(b²−4ac)) / (2a) . Discriminant Δ = b²−4ac: if Δ > 0 → 2 real roots; Δ = 0 → 1 repeated root; Δ < 0 → complex roots. Vertex at x = −b/(2a).

## Frequently Asked Questions

x = (−b ± √(b²−4ac)) / (2a). It solves any quadratic ax²+bx+c=0. The ± means there are two solutions. Enter any real values for a, b, c (a ≠ 0).
Δ = b²−4ac. If Δ > 0: two distinct real roots. If Δ = 0: one repeated real root (tangent to x-axis). If Δ < 0: two complex conjugate roots (no real x-intercepts, parabola doesn't cross x-axis).

Source: https://worldcalculators.org/calculators/quadratic-formula/
Markdown mirror of the HTML page. Prefer this URL for RAG; the interactive calculator still lives on the HTML page.