Math

Symbolic Equation Solver

Solve linear and quadratic equations in x with symbolic steps.

Last validated: Pending

Symbolic Equation Solver parses full one-variable equations and solves them on one page. It supports parentheses, implicit multiplication, powers, and common functions (`sin`, `cos`, `tan`, `exp`, `log`, `ln`, `sqrt`, `abs`) in addition to polynomial terms. For linear and quadratic polynomials, the solver returns symbolic steps and exact-form logic (including discriminant classification). For higher-degree or transcendental equations where closed forms are not applied, it automatically switches to numeric solving and returns approximate real roots. This makes it useful for coursework, engineering checks, and rapid model validation without external CAS tooling.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Equation Input

Enter an equation in x, for example 2x^2 - 5x - 3 = 0, 2(x-1)=4, or exp(x) = 5. Supports parentheses, implicit multiplication, powers, and functions: sin, cos, tan, exp, log, ln, sqrt, abs.

Solution

Normalized: 2x^2 - 5x - 3 = 0

Type: Real

Discriminant: 49

Root 1: 3.0

Root 2: -0.5

Symbolic Steps

Move all terms to one side and simplify.
Quadratic form: 2x^2 - 5x - 3 = 0.
Use x = (-b ± sqrt(b^2 - 4ac)) / (2a).
Discriminant: D = b^2 - 4ac = 49.
D > 0, so there are two distinct real roots.

How to use this tool

Enter an equation in `x` (for example `2(x-1)=4`, `x^3-x-2=0`, or `exp(x)=5`).
Submit the form to parse both sides and normalize as `f(x)=0`.
{"Review the method used"=>"symbolic (linear/quadratic) or numeric approximation."}
Inspect roots and steps, then validate whether approximate roots are acceptable for your use case.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

Equation: 2x^2 - 5x - 3 = 0
Normalized equation: 2x^2 - 5x - 3 = 0
Degree: 2
Solution type: real
Root 1: 3.0
Root 2: -0.5

Expected Outputs

Degree: 2
Discriminant: 49
Root 1: 3
Root 2: -0.5

Interpretation

Degree is 2. Use this as a decision input, not as a standalone conclusion.
Discriminant is 49.0. Use this as a decision input, not as a standalone conclusion.
Root 1 is 3.0. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Scenario A

Equation

Normalized equation

Degree

Solution type

Root 1

Root 2

Scenario B

Equation

Normalized equation

Degree

Solution type

Root 1

Root 2

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

Formula References

Linear equations: solve `bx + c = 0` by isolating `x = -c/b`.
Quadratic formula: `x = (-b ± sqrt(b^2 - 4ac)) / (2a)`.
Discriminant classification: `D > 0` two real roots, `D = 0` repeated root, `D < 0` complex roots.
Numeric fallback: sign-change scan with bisection and Newton refinement for real roots.

Assumptions

Input is interpreted as a polynomial in one variable `x` with real-number coefficients.
Symbolic closed-form solving is guaranteed for degree-1 and degree-2 polynomials.
Higher-degree and transcendental forms return approximate real roots, not exact symbolic families.
Numeric search uses finite windows and may miss roots outside scan range or near singularities.

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Symbolic Equation Solver

Input Pattern

Equation Input

Solution

Symbolic Steps

How to use this tool

Worked Example

Example Inputs

Expected Outputs

Interpretation

Scenario Compare (A vs B)

Scenario A

Scenario B

Confidence and limitations

Formula References

Assumptions

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