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Quadratic Equation Calculator

Find real or complex roots and see which quadratic method fits the equation.

Drag & drop or upload an image or PDF

Enter a quadratic equation, such as 2x^2 - 5x - 3 = 0

Try an example

Choose a method that fits the quadratic

A quadratic equation has degree two and can be written in standard form as ax² + bx + c = 0, where a is not zero. Depending on the coefficients, it may have two real roots, one repeated root, or two complex roots.

Factoring is usually quickest when the roots are simple. Completing the square makes vertex form visible. The quadratic formula works for every quadratic equation and is the safest general method.

How to use the quadratic equation calculator

Enter the problem as written

Type or paste the full expression. You can also upload a clear photo or PDF and check the extracted text before solving.

Read the working, not only the answer

Each transformation is separated and explained so you can compare it with your own method.

Ask about any step

Continue in the same solution to request another method, check a restriction, or ask why a rule applies.

Quadratic formula

The discriminant b² - 4ac tells you whether the roots are real, repeated, or complex.

A reliable way to work through it

Factoring

Rewrite the quadratic as a product and set each factor equal to zero.

Completing the square

Build a perfect square trinomial, then take square roots to isolate x.

Quadratic formula

Substitute a, b, and c carefully. This method works even when the expression does not factor over the integers.

Worked example

Solve 2x² - 5x - 3 = 0

Read the coefficients from standard form.

Compute the discriminant.

Substitute into the quadratic formula.

Evaluate both signs.

The equation has two real roots: x = 3 and x = -1/2.

Common mistakes to check

Using the wrong sign for b

If the equation contains -5x, then b = -5 and -b = 5.

Dividing only the radical

The entire numerator, including -b and the radical, is divided by 2a.

Ignoring complex roots

A negative discriminant gives complex roots rather than no roots.

Related calculators

Factoring CalculatorBreak a polynomial into factors using the pattern that fits, then verify by expanding.Complete the Square CalculatorTurn a quadratic into a perfect square and use it to find vertex form or roots.Polynomial CalculatorWork with polynomial operations, factors, roots, and remainders in one place.Solve for X CalculatorEnter an equation and see how to isolate x, simplify both sides, and check the result.

Questions students ask

Does the calculator show the quadratic formula steps?

Yes. It identifies a, b, and c, evaluates the discriminant, substitutes the values, and simplifies both roots.

Can it solve quadratics that do not factor?

Yes. The quadratic formula and completing the square work when integer factoring does not.

What does the discriminant tell me?

A positive discriminant gives two real roots, zero gives one repeated real root, and a negative value gives two complex roots.

Can I enter a quadratic that is not equal to zero?

Yes. The solver first moves all terms to one side, then solves the resulting standard-form equation.