{"uid":"cap__j4aCJ5AVJEeb4ThC35Pp","slug":"forgemesh-equation-solver-api-b56924e5","name":"Forgemesh Equation Solver API","description":"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.","url":"https://x402.forgemesh.io/solve-equation","method":"POST","headers":{},"bodySchema":{"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"}}},"responseSchema":{"type":"json","example":{"roots":[2,1],"nature":"two real roots","discriminant":1}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.002","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.002/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.002","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_p2_VKeOIxS7GK94EwsVRk","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.002","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Solves linear, quadratic, and 2×2 linear system equations from structured numeric coefficients, returning exact roots including complex roots and discriminant values.","exampleAgentPrompt":"Solve the quadratic equation 2x² + 3x - 5 = 0 — give me the exact roots and the discriminant, including any complex roots if they exist.","exampleUseCases":null,"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T06:59:58.471Z","isFirstParty":false}