Enter the quadratic equation coefficients a, b, c and press the Calculate button:

 Enter a: Enter b: Enter c: The quadratic equation: x2 + x + = 0 Discriminat: Δ  = Quadratic formula: x1,2= First root: x1   = Second root: x2 =

This online calculator is a quadratic equation solver that will solve a second-order polynomial equation such as ax2 + bx + c = 0 for x, where a ≠ 0, using the quadratic formula.

The calculator solution will show work using the quadratic formula to solve the entered equation for real and complex roots. Calculator determines whether the discriminant (b2−4ac) is less than, greater than or equal to 0.

When b2−4ac=0 there is one real root.

When b2−4ac>0 there are two real roots.

When b2−4ac<0 there are two complex roots.

A quadratic is a polynomial of degree two. The quadratic formula is the solution of a second degree polynomial equation of the following form:

Ax² + Bx + C = 0

If you can rewrite your equation in this form, it means that it can be solved with the quadratic formula. A solution to this equation is also called a root of an equation.

The quadratic formula is as follows:

x = (-B ± √Δ)/2A

where:

Δ = B² - 4AC

Using this formula, you can find the solutions to any quadratic equation. Note that there are three possible options for obtaining a result:

1. The quadratic equation has two unique roots when Δ > 0. Then, the first solution of the quadratic formula is x₁ = (-B + √Δ)/2A, and the second is x₂ = (-B - √Δ)/2A.

2. The quadratic equation has only one root when Δ = 0. The solution is equal to x = -B/2A. It is sometimes called a repeated or double root.

3. The quadratic equation has no real solutions for Δ < 0.

You can also graph the function y = Ax² + Bx + C. It's shape is a parabola, and the roots of the quadratic equation are the x-intercepts of this function.