ToolHorizon

Equation Solver (Linear & Quadratic)

📊 Supported Equation Types
Every equation type the solver can handle

Linear Equations

Equations with one variable and degree 1. Find the value of x in a straight-line equation.

Example:3x + 7 = 22 → x = 5

Quadratic Equations

Degree-2 polynomial equations. Solved by factoring, completing the square, or the quadratic formula.

Example:x² - 5x + 6 = 0 → x = 2, 3

Simultaneous Equations

Two equations with two unknowns. Solved using substitution or elimination method.

Example:x+y=10, 2x-y=5 → x=5, y=5

Polynomial Equations

Higher-degree equations (cubic, quartic). The solver finds all real and complex roots.

Example:x³ - 6x² + 11x - 6 = 0

Exponential Equations

Equations where the variable is in the exponent. Solved using logarithms.

Example:2^x = 16 → x = 4

Logarithmic Equations

Equations involving log or ln. Solved by applying log/exponential rules.

Example:log₂(x) = 3 → x = 8
🚀 How to Use
Solve any equation step by step
1

Select Equation Type

Choose the type of equation you want to solve — Linear, Quadratic, Simultaneous, Polynomial, Exponential, or Logarithmic.

2

Enter the Equation

Type your equation into the input field using standard notation. For example: 2x + 5 = 13 or x^2 - 4x + 3 = 0. Use ^ for powers.

3

Click Solve

Hit Solve and the tool calculates all solutions instantly. It shows every step of the solution process, not just the final answer.

4

Review the Step-by-Step Explanation

Read through the worked solution to understand the method used. Copy the answer or save the full working for your assignment or study notes.

💡 Use Cases
Who benefits from the Equation Solver
🎓

Students

Get step-by-step solutions to check homework or understand the method.

📚

Teachers

Generate worked examples and verify answers for worksheets and tests.

⚙️

Engineers

Quickly solve engineering equations during design and analysis work.

💼

Finance

Solve equations for break-even points, pricing models, and financial formulas.

🔬

Scientists

Solve physics and chemistry equations for research and lab work.

🧩

Problem Solving

Tackle puzzle and competition math problems with full solution explanations.

✨ Pro Tips
✏️

Standard Notation

Use * for multiplication (2*x not 2x), ^ for exponents (x^2 not x²), and / for division. Most solvers accept implicit multiplication too — always double check.

📖

Read the Steps

Don't just copy the answer — read every step. Understanding the method is more valuable than the result, especially for exams where you must show working.

Verify Your Answer

After solving, substitute the answer back into the original equation to verify it satisfies both sides. This is a crucial habit for avoiding errors.

🔄

Rearrange First

Before entering a complex equation, rearrange it to standard form (all terms on one side, = 0 on the other). The solver works most reliably with equations in standard form.

❓ Frequently Asked Questions
What is the quadratic formula? +
The quadratic formula solves any equation in the form ax² + bx + c = 0. The solution is: x = (-b ± √(b²-4ac)) / 2a. The part inside the square root (b²-4ac) is called the discriminant. If it's positive, there are 2 real solutions. If zero, one real solution. If negative, two complex solutions.
What are simultaneous equations? +
Simultaneous equations are a set of two or more equations that share the same unknown variables. Solving them means finding values for all unknowns that satisfy all equations at once. Common methods are substitution (express one variable in terms of the other) and elimination (add/subtract equations to remove one variable).
Can the solver handle equations with no solution? +
Yes. If an equation has no real solution (e.g. x² + 1 = 0, which only has complex roots), the solver will indicate this and may show the complex solutions. If a system of simultaneous equations is inconsistent (no solution) or has infinite solutions, the solver will identify and explain this.
Can I solve equations with fractions or decimals? +
Yes. Enter fractions as (1/2) or use decimal notation (0.5). The solver handles rational coefficients accurately. For best results with fractions, use parentheses to clearly group the numerator and denominator.
Does the solver show the working or just the answer? +
Both. The solver shows the complete step-by-step solution process — each algebraic manipulation is shown and explained in plain language. This makes it useful both for getting quick answers and for understanding the method.
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