Maths Solver

ax² + bx + c = 0
ax + b = cx + d
1) a₁x + b₁y = c₁
2) a₂x + b₂y = c₂

Introduction of Tool

Math can be intimidating, especially when you're staring at an equation that just doesn't make sense. I built this Maths Solver to act as a bridge between confusion and clarity. Whether you are a student struggling with algebra homework, a teacher preparing examples, or just someone trying to figure out a discount calculation, this tool is designed to give you the answer immediately and show you how we got there.

It handles the most common "stuck points" in math: finding the roots of a quadratic equation, solving for a single variable, finding the intersection of two lines, and handling tricky percentage problems. No ads, no sign-up, just pure math.

How to Use This Tool

The tool is divided into four tabs based on the type of problem you are facing.

  • Quadratic Equation: Enter the values of a, b, and c from the equation ax² + bx + c = 0. The tool will tell you if the roots are real or complex.
  • Linear Equation: Perfect for equations like 2x + 5 = 15 or variables on both sides like 3x - 2 = x + 4. Enter the coefficients for the left and right sides.
  • System of Equations: Use this when you have two variables (x and y) and two equations. Enter the coefficients for both equations to find the point where the lines cross.
  • Percentage: Select what you want to find (e.g., "What is 20% of 50?") and enter the numbers.

Feature List

  • Complex Number Support: The quadratic solver doesn't just say "No Solution" if the discriminant is negative. It calculates the imaginary roots (e.g., 3 + 2i).
  • Step-by-Step Logic: For the quadratic solver, the tool displays the value of the discriminant (Delta) so you can verify your manual calculations.
  • Instant Validation: The linear solver automatically checks if the variables cancel out (Infinite solutions) or if the equation is impossible (No solution).
  • Percentage Modes: Covers all three types of percentage questions, not just one.

Benefits of Using This Tool

  • Accuracy Check: Use it to double-check your manual homework. If you got x=5 and the calculator got x=5, you're good. If not, you know where to look for errors.
  • Time Saver: Solving a system of equations by substitution or elimination takes time. This tool does it in milliseconds.
  • Learning Aid: By seeing the structure of the solution, you can start to recognize patterns in how equations work.

Examples / Sample Calculations / Demo

Here is how the solver handles real-world math problems.

Quadratic Example: A ball is thrown upwards. Its height is -5t² + 20t + 2. When does it hit the ground (h=0)?
Enter a=-5, b=20, c=2. The solver gives two roots, one negative (ignore) and one positive (~4.1 seconds).

System Example: Comparing two mobile plans. Plan A: 10x + 50. Plan B: 15x + 20. Where is the cost equal?
Enter the coefficients. The solver finds x=6. After 6 months, Plan B becomes more expensive.

Common Mistakes / FAQs

What does "i" mean in the quadratic result?

"i" stands for the imaginary unit (√-1). If the discriminant is negative, the equation has no real roots (the parabola doesn't touch the x-axis), but it does have complex roots.

What if the linear solver says "Infinite Solutions"?

This happens when the equations on the left and right sides are identical. For example, 2x + 3 = 2x + 3. Any value of x will make this true.

How do I calculate a 15% discount?

Use the "Percentage" tab. Select "What is X% of Y?". Enter 15 for X and your price for Y. The result is the discount amount. Subtract this from the original price to get the final cost.

Related Tools / You May Also Like

How It Works / Behind the Scenes

The tool relies on algebraic algorithms programmed in JavaScript.

  • Quadratic: Calculates the discriminant Δ = b² - 4ac. It then applies the quadratic formula. If Δ < 0, it splits the square root of the negative number into a real part and an imaginary part.
  • Linear: Rearranges terms to get ax = b, then divides. It handles the case where a = 0 separately.
  • System: Uses Cramer's Rule (determinants) or algebraic substitution to solve for x and y simultaneously.

User Testimonials / Reviews / Feedback

  • "I use this to check my daughter's algebra homework. It's faster than me working it out on paper!" — David R.
  • "The percentage solver saved me during my black Friday shopping calculations." — Jessica M.

Tips & Tricks / Pro Guide

  • Check Your Signs: In math, a negative sign changes everything. If you get a weird result, check if you entered -5 instead of 5.
  • Decimals vs Fractions: This solver uses decimals for precision. If you have fractions (like 1/3), convert them to decimals (0.333) before entering them.
  • Use Linear for Budgeting: You can use the linear solver to find a break-even point. Cost = Revenue.

Printable / Export Option

Need to show your work? Use Ctrl+P. The layout hides the buttons and menus, printing a clean sheet with your equation inputs and the final solution steps.

History / Version Updates / Change Log

  • Version 1.0: Basic Quadratic and Linear solvers.
  • Version 2.0: Added Complex Number support for imaginary roots.
  • Version 3.0 (Current): Added System of Equations (2 variables) and the Percentage Solver module.