Quadratic Equation Calculator
Quadratic Equation Solver works out Root 1 (real part) and Root 2 (real part) from Input style, a (coefficient of x^2) and b (coefficient of x). The default figures on this page give root 1 (real part) of -0; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
5 steps
- Standard form: x^2 = 0 with a = 1, b = 0, c = 0.
- Discriminant D = b^2 - 4ac = 0^2 - 4(1)(0) = 0.
- D = 0, so the parabola touches the axis once at x = 0 / 2 = 0.
- Vertex: x = -b/(2a) = 0, y = c - b^2/(4a) = 0.
- Vieta's formulas: sum of roots = -b/a = 0, product = c/a = 0.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Quadratic Equation Solver calculates
Solves ax^2 + bx + c = 0 for real or complex roots and reports the discriminant, vertex, axis of symmetry, factored form and vertex form.
How to use this Quadratic Equation Solver
Enter Input style, a (coefficient of x^2), b (coefficient of x) and c (constant term). Root 1 (real part) updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Root 1 (real part), Root 2 (real part) and Root 1 (imaginary part).
The method follows OpenStax, College Algebra 2e, Section 2.5: Quadratic Equations and Press, Teukolsky, Vetterling & Flannery, Numerical Recipes, 3rd ed., Section 5.6 "Quadratic and Cubic Equations".
x^2 - 5x + 6 = 0 example
With a (coefficient of x^2): 1, b (coefficient of x): -5, c (constant term): 6, the calculator returns Root 1 (real part): 3, Root 2 (real part): 2, Discriminant b^2 - 4ac: 1. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Root 1 (real part), Root 2 (real part) and Root 1 (imaginary part). The inputs you can vary are Input style, a (coefficient of x^2), b (coefficient of x), c (constant term), Equation and Variable.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to get a quadratic equation on a calculator?
Solves ax^2 + bx + c = 0 for real or complex roots and reports the discriminant, vertex, axis of symmetry, factored form and vertex form. Open “How this is worked out” beside the result to see each step for your own figures.
Can a TI-84 solve a quadratic?
Solves ax^2 + bx + c = 0 for real or complex roots and reports the discriminant, vertex, axis of symmetry, factored form and vertex form. On the figures this page opens with — a (coefficient of x^2) 1, b (coefficient of x) -5 and c (constant term) 6 — the root 1 (real part) is -0. Put your own figures in their place and the working updates beside the result.
Can you put the quadratic formula into a calculator?
It needs Input style, a (coefficient of x^2), b (coefficient of x), c (constant term), Equation and Variable. Nothing else is required, and the figures stay in your browser.
Is there a quadratic formula button on a calculator?
The result gives Root 1 (real part), Root 2 (real part), Root 1 (imaginary part), Root 2 (imaginary part), Roots and Discriminant b^2 - 4ac, each labelled with its unit so the figure can be read on its own.
How do you put a quadratic formula into your calculator?
The page opens with worked default figures: root 1 (real part) of -0. Replace them with your own and every figure updates as you type.
How to calculate a quadratic equation step by step?
A checked example is built in: Root 1 (real part): 3. It is recomputed on every release, so the method on this page is tested rather than asserted.