Calculadora de Álgebra
Resuelve ecuaciones lineales y cuadráticas paso a paso
Algebra Calculator
Solve quadratic equations ax² + bx + c = 0
Find roots of ax² + bx + c = 0
x = (-b +/- sqrt(b² - 4ac)) / 2aWhat is an Algebra Calculator?
An Algebra Calculator is a math tool that helps you work with algebraic expressions and equations quickly and accurately. Algebra is the branch of mathematics that uses variables (like x, y, or z) to represent unknown values and uses rules to simplify expressions, solve equations, factor polynomials, and expand or rearrange terms.
Instead of doing long manual steps—like combining like terms, distributing parentheses, or solving for a variable—an algebra calculator can perform these operations instantly. This is especially helpful for checking homework, verifying steps in a math problem, or exploring 'what-if' scenarios by changing values.
Algebra calculators are commonly used in middle school and high school math (pre-algebra, algebra 1/2), as well as in college courses like calculus, physics, chemistry, economics, and engineering—anywhere equations and formulas need to be simplified or solved.
How to Use This Algebra Calculator
- Enter your expression or equation -- Example expressions: 3x + 2x - 7 or 2(x + 4) - 3x. Example equations: 2x + 5 = 17.
- Choose the operation (if applicable) -- such as Simplify, Solve, Factor, Expand, or Evaluate.
- Select the variable (if applicable) -- for example, solve for x.
- Click 'Calculate' -- the calculator will produce the simplified form or solution.
- Review the result -- some calculators also show steps; if shown, use them to learn the process.
Tips:
- Use parentheses to clearly group terms: 2(x + 3)
- Use ^ for exponents if supported: x^2
- If you get an unexpected result, double-check signs and parentheses (most mistakes come from missing parentheses or negative signs)
Algebra Formulas
Combining Like Terms
Like terms have the same variable part (same variables raised to the same powers):
- 3x + 2x = 5x
- 7a² − 4a² = 3a²
Distributive Property
Rule: a(b + c) = ab + ac
Example: 2(x + 5) = 2x + 10
Solving a Linear Equation
General form: ax + b = c
Solve for x: x = (c − b) / a
Isolate x by subtracting b, then dividing by a
Factoring a Quadratic
Form: x² + bx + c
Find two numbers that multiply to c and add to b:
x² + bx + c = (x + m)(x + n)
Quadratic Formula (Solving ax² + bx + c = 0)
x = (−b ± √(b² − 4ac)) / 2a
The expression b² − 4ac is the discriminant, which determines the number and type of solutions:
- Discriminant > 0: two distinct real roots
- Discriminant = 0: one repeated real root
- Discriminant < 0: two complex (imaginary) roots
Example Calculations
Example 1: Simplify an expression
Expression: 3x + 2x − 7
Step: Combine like terms: 3x + 2x = 5x
Answer: 5x − 7
Example 2: Expand using distribution
Expression: 2(x + 4) − 3x
Step 1: Distribute: 2(x + 4) = 2x + 8
Step 2: Subtract 3x: (2x + 8) − 3x = −x + 8
Answer: 8 − x
Example 3: Solve a linear equation
Equation: 2x + 5 = 17
Step 1: Subtract 5 from both sides: 2x = 12
Step 2: Divide by 2: x = 6
Answer: x = 6
Example 4: Factor a quadratic
Expression: x² + 5x + 6
Step: Find two numbers that multiply to 6 and add to 5 → 2 and 3
Answer: (x + 2)(x + 3)
Frequently Asked Questions
What is a variable in algebra?
A variable is a symbol (like x or y) that represents an unknown or changeable value. For example, in 2x + 3, the value of x can vary.
What does it mean to 'simplify' an expression?
Simplifying means rewriting an expression in a cleaner form by combining like terms, reducing fractions, and removing unnecessary parentheses—without changing its value.
What’s the difference between an expression and an equation?
An expression does not have an equals sign (example: 3x + 2). An equation includes an equals sign and states two things are equal (example: 3x + 2 = 11).
Why do I need parentheses?
Parentheses show grouping and control the order of operations. For example, 2(x + 3) is different from 2x + 3.
Can an algebra calculator solve any equation?
Many can solve common types (linear, some quadratics, basic systems), but very complex equations may have restrictions depending on the tool. If your equation doesn’t solve, try simplifying it first or confirm the calculator supports that equation type.
Want to add this algebra calculator to your website? Get a custom embed code that matches your site's design and keeps visitors engaged.
¿Qué es el Álgebra?
El álgebra es la rama de las matemáticas que utiliza símbolos — generalmente letras como x e y — para representar cantidades desconocidas y las relaciones entre ellas. Es la base de prácticamente todo campo cuantitativo: la ciencia la usa para sus fórmulas, la ingeniería para modelar sistemas, las finanzas para calcular rendimientos y riesgos, y la programación para diseñar algoritmos y lógica. Entender el álgebra significa saber trabajar con incógnitas y expresar reglas de forma general y reutilizable.
Resolver una ecuación significa encontrar el valor específico de x (o cualquier variable) que hace que ambos lados sean iguales. Las ecuaciones lineales tienen exactamente una solución porque la variable aparece solo en la primera potencia. Las ecuaciones cuadráticas — donde la variable está al cuadrado — pueden tener cero, una o dos soluciones reales, dependiendo de si la parábola que representan cruza, toca o no intersecta el eje x. Esta calculadora maneja ambos tipos y te muestra exactamente cómo llegar al resultado.
Cómo Usar la Calculadora de Álgebra
- Selecciona el tipo de ecuación — Lineal (ax + b = 0) o Cuadrática (ax² + bx + c = 0).
- Ingresa los coeficientes a, b y c en sus campos correspondientes. Para ecuaciones lineales, solo se necesitan a y b.
- Haz clic en el botón Resolver para calcular la(s) solución(es).
- Lee el resultado — la calculadora muestra cada raíz y, para cuadráticas, el valor del discriminante.
Fórmulas Utilizadas
Lineal: ax + b = 0 → x = -b / a
Cuadrática: ax² + bx + c = 0
x = (-b ± √(b² - 4ac)) / 2a
Discriminante: Δ = b² - 4ac
Δ > 0 → dos raíces reales distintas
Δ = 0 → una raíz real (raíz doble)
Δ < 0 → sin raíces reales (raíces complejas)La fórmula cuadrática es universal — funciona para cualquier ecuación cuadrática sin importar si se factoriza fácilmente. Cuando el discriminante Δ es negativo, la ecuación no tiene soluciones reales; las raíces son números complejos que involucran la unidad imaginaria i.
Ejemplos Resueltos
Ejemplo 1 — Lineal: 2x + 6 = 0
Reordenamos a forma estándar: 2x + 6 = 0, entonces a = 2, b = 6. Aplicando x = -b / a obtenemos x = -6 / 2 = -3. Verificación: 2(-3) + 6 = -6 + 6 = 0. Correcto.
Ejemplo 2 — Cuadrática: x² - 5x + 6 = 0
Coeficientes: a = 1, b = -5, c = 6. Discriminante: Δ = (-5)² - 4(1)(6) = 25 - 24 = 1. Como Δ > 0, hay dos raíces reales: x = (5 ± 1) / 2, dando x = 3 y x = 2. Ambas satisfacen la ecuación.
Ejemplo 3 — Sin Solución Real: x² + 4 = 0
Coeficientes: a = 1, b = 0, c = 4. Discriminante: Δ = 0² - 4(1)(4) = -16. Como Δ < 0, no hay soluciones reales. Las raíces son los números complejos x = ±2i.