A quadratic equation calculator solves equations of the form ax² + bx + c = 0. Enter the values of a, b and c, and it finds the roots using the quadratic formula, showing the discriminant and each step. It also handles complex roots when the equation has no real solutions.
The quadratic formula is x = (−b ± √(b² − 4ac)) ÷ 2a. The expression b² − 4ac is the discriminant. If it’s positive, there are two real roots; if it’s zero, there’s one repeated root; if it’s negative, there are two complex roots. For example, 2x² − 4x − 6 = 0 has a = 2, b = −4, c = −6. The discriminant is 16 + 48 = 64, so x = (4 ± 8) ÷ 4, giving x = 3 and x = −1.
Other methods include factoring, which is fastest when it works (2x² − 4x − 6 = 2(x − 3)(x + 1)), and completing the square, which is how the quadratic formula is derived. Graphing shows the roots as the points where the parabola crosses the x-axis.
Common mistakes: forgetting the negative sign on b, mishandling the ± (which gives two answers), and dividing only part of the numerator by 2a. Always check your answers by plugging them back into the original equation.
Tips for getting accurate results from the Quadratic Equation Calculator: double-check that every input uses the right units, enter numbers without commas or symbols, and run the calculation a second time with a quick estimate in your head to confirm the answer looks reasonable.
How to use the Quadratic Equation Calculator on Minedit: enter your values in the fields, press calculate, and review the step-by-step breakdown under the result. If something looks off, change one input at a time to see how it affects the answer, which is also a great way to learn the math behind it.
Learn more on Wikipedia’s quadratic formula article. Find axis of symmetry, factoring and radical calculators on Minedit.