CALCULATE WITH CONFIDENCE

Algebra & Equations

Quadratic Formula Calculator

Calculate quadratic formula with validated inputs and explicit results.

Algebra & Equations

Enter values

Private calculation in your browser
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Use the notation shown in each label and example. Inputs stay on this device and are never sent to a calculation service.

Result

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Enter valid values to see the result.

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Understand the subject

What is Quadratic Formula?

An equation states that two expressions have the same value. Solving means finding values that keep that balance true.

Use it to expose the allowed unknown value instead of changing one side without preserving equality.

The relationship

Write the rule before calculating

See the structure

What the calculation is doing

Worked interpretation

Read the result in context

Enter the example values shown in the fields to verify the stated relationship.

Interpret with care

Important boundary

An algebraic step is valid only when it applies equally to both sides and does not divide by a possible zero quantity.

Use the Mathematics collection to move between connected concepts without duplicating the calculation.

Understand the subject

What is a quadratic equation?

A quadratic equation contains a nonzero squared term. Its graph is a parabola, and its real roots are the x-values where the parabola crosses the horizontal axis.

Use the quadratic formula when factoring is unclear or when exact radical roots are needed.

The relationship

The defining equation

The discriminant Δ=b²−4ac determines whether there are two, one, or no real roots.

See the structure

The discriminant predicts the crossings

Worked example

Solve x²−5x+6=0

Δ=1, so x=(5±1)/2 and x=2 or 3

Interpret with care

What the result does—and does not—mean

The coefficient a must be nonzero. A negative discriminant requires complex-number roots, outside a real-only result mode.

Quick guide

How to use this calculator

  1. Enter values using the notation shown beside each field.
  2. Choose a calculation mode when the tool offers more than one interpretation.
  3. Read the primary answer first, then inspect the supporting details.

Calculation method

Apply the stated definition

Δ = b² − 4ac; x = (−b ± √Δ)/(2a)

The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.

Worked example

Worked example

Enter the example values shown in the fields to verify the stated relationship.

Δ = b² − 4ac; x = (−b ± √Δ)/(2a)

Supported inputs

Precision and limits

Finite, bounded input

Numeric inputs use finite JavaScript floating-point values with magnitude limits. Results are normally displayed to 12 significant digits; outputs labelled approximate are not exact identities.

Notation

Enter ordinary finite decimals. Polynomial fields use coefficients in descending powers, separated by commas; for example 1, −3, 2 means x² − 3x + 2.