Equation Solver - Hindi Numerals
Solve linear, quadratic, and other mathematical equations with step-by-step solutions with Hindi numeral system support.
About This Numeral System
Hindi numerals (० through ९) are the digits of the Devanagari script, used for Hindi, Marathi, Nepali, and several other languages of South Asia. They are the numeral system most commonly encountered in India for Hindi-language documents, education, media, and government publications. This calculator displays results in Devanagari numerals for users who read and write in Hindi or other Devanagari-script languages.
A free online equation solver that handles linear equations, quadratic equations, polynomial equations up to degree 4, and systems of linear equations with multiple unknowns. The solver uses both symbolic methods (for exact algebraic solutions like x = √2) and numerical methods (for transcendental equations like sin(x) = x that have no closed-form solution). Step-by-step solutions show the method used — whether it is the quadratic formula, factoring, Gaussian elimination, or Newton's method — so you can follow the reasoning, not just get the answer.
How This Calculator Works
Equation Solving Methods: Quadratic: x = (−b ± √(b²−4ac)) / 2a | Newton: x_{n+1} = x_n − f(x_n)/f'(x_n)
Linear equations are solved by Gaussian elimination. Quadratic equations use the quadratic formula. Polynomials up to degree 4 use factoring and numerical root-finding. Transcendental equations (e.g. sin(x) = x) use Newton's method, which iteratively refines an initial guess using the function value and its derivative until convergence.
Frequently Asked Questions
What types of equations can the solver handle?
The equation solver can solve linear equations (e.g., 2x + 5 = 13), quadratic equations (e.g., x² - 5x + 6 = 0), polynomial equations, systems of linear equations, and general numerical equations. It supports both algebraic (symbolic) and numerical solving methods.
How do I solve a quadratic equation?
Enter your quadratic equation in the form ax² + bx + c = 0 (e.g., "x^2 - 5x + 6 = 0"). The solver will find all real and complex roots using the quadratic formula or factoring. For the example given, the solutions are x = 2 and x = 3.
Can I solve systems of equations with multiple variables?
Yes! Use the linear system solver mode to enter multiple equations with multiple unknowns. For example, to solve (2x + y = 7, x - y = 2), the solver will find x = 3 and y = 1. The solver uses methods like Gaussian elimination or Cramer's rule.
What is the difference between symbolic and numerical solving?
Symbolic solving finds exact algebraic solutions (like x = √2 or x = 3/4), while numerical solving finds decimal approximations (like x ≈ 1.414 or x = 0.75). For complex equations without closed-form solutions, numerical methods like Newton's method are used.
How do I solve an equation with no closed-form solution?
For equations like sin(x) = x or transcendental equations, use the numerical solver. Enter your equation, provide an initial guess (starting point), and the solver will iteratively find the approximate solution using numerical methods. The accuracy depends on the precision settings.
Can the solver handle polynomial equations of any degree?
The solver can handle polynomials up to degree 4 (quartic) with symbolic solutions, and higher-degree polynomials with numerical approximations. For cubic and quartic equations, it uses specialized formulas. For degree 5 and above, numerical methods are employed.
What should I do if the solver shows "no solution"?
This means the equation has no real solutions. For example, x² = -1 has no real solutions (but has complex solutions ±i). Check your equation for typos, verify it's mathematically valid, or try using the complex number mode if you need complex solutions.
Does this calculator support Nepali and Marathi numerals?
Yes. Nepali and Marathi use the same Devanagari numeral glyphs (०–९) as Hindi. If you read or write in those languages, the Hindi numeral mode will display numbers correctly.
Worked Examples
Input: Solve x² − 5x + 6 = 0
Result: Using quadratic formula: x = (5 ± √(25−24)) / 2 = (5 ± 1) / 2. Roots: x = 3 and x = 2.
Key Features
- Linear and quadratic equations
- Systems of 2 and 3 unknowns
- Step-by-step solutions
- Numerical and symbolic roots
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