{"uid":"cap_gF46PWbHvNCcOiIpahLS9","slug":"forgemesh-equation-solver-4645fe87","name":"ForgeMesh Equation Solver","description":"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.","url":"https://x402.forgemesh.io/equation-solver","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_HGKhRT7Tqo1H2YG573cl2","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 equations, quadratic equations, and 2-variable linear systems, returning exact real or complex roots from structured coefficients.","exampleAgentPrompt":"Solve the quadratic equation 2x² + 5x - 3 = 0 and give me the exact roots, including complex ones if needed.","exampleUseCases":null,"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T06:59:27.614Z","isFirstParty":false}