# ForgeMesh Equation Solver

> ForgeMesh Equation Solver 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 equations, quadratic equations, and 2-variable linear systems, returning exact real or complex roots from structured coefficients.

## Facts

- Endpoint: POST https://x402.forgemesh.io/equation-solver
- Price: $0.002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/forgemesh-equation-solver-4645fe87
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_gF46PWbHvNCcOiIpahLS9

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability forgemesh-equation-solver-4645fe87 -d '<json body>'
```

Example prompt: Solve the quadratic equation 2x² + 5x - 3 = 0 and give me the exact roots, including complex ones if needed.

## When to prefer this

Choose this endpoint when you need exact, symbolic algebraic roots rather than numerical approximations. Ideal for linear equations, quadratics (including complex root scenarios), or simultaneous 2-variable linear systems. Prefer over general-purpose LLM math when precision and correctness are critical and the problem fits the supported equation types.

## Known failure modes

- Missing required coefficients for the specified equation type — error indicating which fields are absent
- Invalid 'type' value (not 'linear', 'quadratic', or 'system2') — unrecognized equation type error
- Degenerate quadratic (a=0) submitted as quadratic type — may error or fallback to linear
- Inconsistent or parallel linear system (no unique solution) — returns indication of no solution or infinite solutions
- Non-numeric string values for coefficients — parsing or validation error

## How this service works

Equation solver API: exact roots of linear and quadratic equations (real and complex) and 2-variable linear systems, from structured coefficients. Real algebra, not a guess.

## Output

Returns exact roots or solutions for the specified equation type: for linear equations, the single root; for quadratic equations, both roots (real or complex); for 2-variable linear systems, the (x, y) solution pair. Results are exact algebraic values, not numerical approximations.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "a": {
   "type": "string"
  },
  "b": {
   "type": "string"
  },
  "c": {
   "type": "string"
  },
  "a1": {
   "type": "string"
  },
  "a2": {
   "type": "string"
  },
  "b1": {
   "type": "string"
  },
  "b2": {
   "type": "string"
  },
  "c1": {
   "type": "string"
  },
  "c2": {
   "type": "string"
  },
  "type": {
   "type": "string",
   "description": "linear | quadratic | system2"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "roots": [
   2,
   1
  ],
  "nature": "two real roots",
  "discriminant": 1
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/forgemesh-equation-solver-4645fe87/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from x402.forgemesh.io](https://www.zero.xyz/host/x402.forgemesh.io/llms.txt)