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Forgemesh Equation Solver API
x402
Forgemesh Equation Solver API is a paid API for AI agents from x402.forgemesh.io, paid per call via x402, $0.002/call, status unknown (last checked 2026-09-15).
Solves linear, quadratic, and 2×2 linear system equations from structured numeric coefficients, returning exact roots including complex roots and discriminant values.
Price / call$0.002
Success—
StatusUnknown
How this service works
Equation solver API: solve linear (ax+b=0), quadratic (ax²+bx+c=0, with real OR complex roots and the discriminant), and 2×2 linear systems — from structured numeric coefficients, not a parsed string. Exact roots every time. For engineering, education, and scientific agents.
Output
Returns exact roots for the specified equation type: for linear (ax+b=0) the single root x, for quadratic (ax²+bx+c=0) two roots (real or complex) plus the discriminant, for a 2×2 linear system the values of both unknowns.
Example use cases
Example prompt
“Solve the quadratic equation 2x² + 3x - 5 = 0 — give me the exact roots and the discriminant, including any complex roots if they exist.”
Technical details
Endpoint
POSThttps://x402.forgemesh.io/solve-equationWhen to prefer
Choose this endpoint when you need exact algebraic roots from structured numeric coefficients — not a natural language expression parser — for linear, quadratic, or 2×2 systems. Prefer it over general-purpose math APIs when you require discriminant values, complex root support, or deterministic numeric outputs for engineering or educational pipelines.
Side effects
- Missing required coefficients for the selected equation type returns a validation error
- Invalid or non-numeric coefficient strings cause parsing failure
- Division by zero if leading coefficient a=0 for quadratic or system is degenerate (no unique solution)
- Unrecognized 'type' value (not 'linear', 'quadratic', or 'system2') returns an error
- Payment failure or insufficient USDC balance prevents the call from completing
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| a | string | |
| b | string | |
| c | string | |
| a1 | string | |
| a2 | string | |
| b1 | string | |
| b2 | string | |
| c1 | string | |
| c2 | string | |
| type | string | linear | quadratic | system2 |
Output
Schema · Response
{
"type": "json",
"example": {
"roots": [
2,
1
],
"nature": "two real roots",
"discriminant": 1
}
}Tags
x402
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