{
  "slug": "quadratic",
  "title": "Quadratic Equation Solver",
  "heading": "Quadratic Equation Solver",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/quadratic",
  "summary": "Solve ax² + bx + c = 0.",
  "description": "Computes both roots of a quadratic and reports complex roots when the discriminant is negative.",
  "formula": null,
  "dateModified": "2026-10-03",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=quadratic",
  "inputs": [
    {
      "id": "a",
      "label": "a",
      "kind": "number",
      "hint": null,
      "default": 1,
      "unit": null,
      "min": null,
      "max": null
    },
    {
      "id": "b",
      "label": "b",
      "kind": "number",
      "hint": null,
      "default": -5,
      "unit": null,
      "min": null,
      "max": null
    },
    {
      "id": "c",
      "label": "c",
      "kind": "number",
      "hint": null,
      "default": 6,
      "unit": null,
      "min": null,
      "max": null
    }
  ],
  "outputs": [
    {
      "id": "x1",
      "label": "Root 1",
      "format": "raw",
      "hint": null,
      "primary": true
    },
    {
      "id": "x2",
      "label": "Root 2",
      "format": "raw",
      "hint": null,
      "primary": false
    },
    {
      "id": "discriminant",
      "label": "Discriminant",
      "format": "decimal",
      "hint": null,
      "primary": false
    }
  ],
  "worked_example": {
    "inputs": [
      "a: 1",
      "b: -5",
      "c: 6"
    ],
    "outputs": [
      "Root 1: 3.000000",
      "Root 2: 2.000000",
      "Discriminant: 1"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter a.",
      "Enter b.",
      "Enter c.",
      "Read your root 1 on the right — it updates as you type.",
      "Hit Share to keep the scenario or send it to someone."
    ]
  },
  "scenarios": [
    {
      "name": "Conservative",
      "description": "Lower-end numbers — what if things land soft?",
      "values": {
        "a": 0.6,
        "b": -3,
        "c": 3.5999999999999996
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "a": 1,
        "b": -5,
        "c": 6
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "a": 1.6,
        "b": -8,
        "c": 9.600000000000001
      }
    }
  ],
  "limitations": [
    "Results are rounded for display; the underlying calculation keeps full precision.",
    "Very large or very small inputs may hit floating-point limits in the browser.",
    "Inputs outside the accepted range are clamped rather than rejected."
  ],
  "faq": [
    {
      "q": "How does the quadratic equation solver work?",
      "a": "Computes both roots of a quadratic and reports complex roots when the discriminant is negative."
    },
    {
      "q": "What do I need to enter?",
      "a": "3 values: a, b, and c. Each field starts with a sensible default, so you can change one number at a time and watch the result move."
    },
    {
      "q": "What does the root 1 result mean?",
      "a": "It is returned as a plain value and updates live as you edit the inputs, so you can compare two or three versions of a scenario in a few seconds."
    },
    {
      "q": "Is this calculator free, and do I need an account?",
      "a": "Yes, it's free, and no account is required. Nothing you type is stored on our servers — the maths runs entirely in your browser."
    },
    {
      "q": "How accurate is the result?",
      "a": "It applies the standard formula exactly, so the arithmetic is precise. Results are rounded for display; the underlying calculation keeps full precision."
    },
    {
      "q": "Who is this tool for?",
      "a": "It's built for students, developers, and anyone who needs the answer right now without setting up a spreadsheet."
    }
  ],
  "related": [
    "https://www.revenuelab.fyi/toolbox/exponent",
    "https://www.revenuelab.fyi/toolbox/slope"
  ],
  "license": "CC-BY-4.0",
  "citation": "RevenueLab — Quadratic Equation Solver (https://www.revenuelab.fyi/toolbox/quadratic)"
}