Quadratic equations have the form ax2 + bx + c = 0
They will generally have two solutions; that is, two different values of x that make the equation true.

It can happen that both solutions are the same number, and it is possible
that the solutions will be complex or imaginary numbers.

To use this utility, you type in values for a, b, and c in the boxes below, and press the Calculate button.
You may enter positive, negative, or zero values, but the value of a cannot be zero.
A blank or non-numeric character is treated as a zero.

 a b c x2 + x + = 0

Solutions

x1 =
x2 =

Other Information

Discriminant =
Parabola opens
Vertex:

Factoring (real factors only)

The quadratic trinomial ax2 + bx + c factors into:

Enter the coefficients for the Ax2 + Bx + C = 0 equation and
Quadratic Equation will output the solutions (if they are not imaginary).

Ax2 + Bx + C = 0
 A = B = C =
 x1 = x2 =

If A = 0, the equation is not quadratic.

Examples for easy calculations:

 Equation: x1 x2 x2 − 2x − 8 = 0 4 −2 2x2 + 3x − 20 = 0 2.5 −4 2x2 + 18 = 0 0 −9 x2 + 5x − 14 = 0 2 −7 3x2 + 36x − 39 = 0 1 −13 9x2 − 82x + 9 = 0 9 1/9 8x2 + 39x − 5 = 0 1/8 −5 6x2 − 12x − 6 = 0 2.414 −0.414 2.5x2 + 17.5x − 20 = 0 1 −8 49x2 + 154x + 21 = 0 −1/7 −3 4x2 + (107/3)x − 3 = 0 1/12 −9 2x2 − 20.8x + 8 = 0 10 2/5 12x2 + x − 1 = 0 − 1/4 1/3 3x2 + 9x − 12 = 0 1 −4 5x2 − 2x − 3/5 = 0 3/5 −1/5 x2 − 0.9x + 0.7 = 0 1.4 − 0.5 5x2 − 16.5x + 13 = 0 −1.3 −2 0.5x2 − 8x + 32 = 0 8 8