QUADRATIC FORMULA CALCULATOR
"Solve quadratic equations instantly with the Free Quadratic Formula Calculator. Enter coefficients a, b, and c and get accurate roots — perfect for math homework, engineering, or algebra practice."
➗ Quadratic Formula Calculator — Solve Quadratic Equations Fast
Welcome to the Free Quadratic Formula Calculator on calculator.cl! This tool helps you find the solutions (roots) of quadratic equations of the form:
ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0
Whether you’re doing math homework, studying algebra, or solving problems in science and engineering, this calculator gives you accurate roots instantly — no login required.
🧠 What Is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree two, meaning it contains an x2x^2x2 term. These equations appear in various areas, including physics, finance, and optimization problems.
The general form is:
ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0
where:
aaa, bbb, and ccc are constants
a≠0a \neq 0a=0
📐 Quadratic Formula
The solutions (roots) of a quadratic equation are found using the quadratic formula:
x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac
This formula works for all quadratic equations — whether the roots are real or complex.
🧮 How It Works
To use this calculator:
Enter the coefficient a
Enter the coefficient b
Enter the coefficient c
Click Calculate
The tool computes:
The discriminant (b2−4acb^2 - 4acb2−4ac)
The two possible roots using the formula
Whether roots are real or complex
Results display instantly so you can see both solutions clearly.
📊 Example Calculation
Let’s say you have the equation:
2x2−4x−6=02x^2 - 4x - 6 = 02x2−4x−6=0
Plugging in:
a=2a = 2a=2
b=−4b = -4b=−4
c=−6c = -6c=−6
The calculator applies:
x=−(−4)±(−4)2−4(2)(−6)2(2)x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-6)}}{2(2)}x=2(2)−(−4)±(−4)2−4(2)(−6) x=4±16+484=4±644x = \frac{4 \pm \sqrt{16 + 48}}{4} = \frac{4 \pm \sqrt{64}}{4}x=44±16+48=44±64 x1=4+84=3andx2=4−84=−1x_1 = \frac{4 + 8}{4} = 3\quad \text{and}\quad x_2 = \frac{4 - 8}{4} = -1x1=44+8=3andx2=44−8=−1
So the roots are 3 and −1.
📍 Why This Calculator Is Useful
This tool is ideal for:
Students solving algebra problems
Teachers checking answers quickly
Engineers analyzing quadratic systems
Anyone needing accurate roots instantly
Avoid manual errors and time-consuming steps — get instant results every time.
💡 Tips for Best Results
Double-check input values of aaa, bbb, and ccc.
If the discriminant is negative, the calculator will return complex roots.
Use the calculator to spot-check manual solutions or homework.
⚠️ Important Notes
The calculator handles both real and complex roots.
For extremely large coefficients, results may include decimals — check precision if needed.
TO USE THIS TOOL VISIT https://calculator.cl/quadratic-formula-calculator/ OR SCAN THIS QR CODE .
