· x2 +   · x +   = 0

 x1 = - i · x2 = - i ·

Δ =

xS =   yS =

The results are rounded to significant digits.

With this calculator you can solve quadratic equations of the type a·x2 + b·x + c = 0. In addition, the discriminant Δ = b2 - 4·a·c and the coordinates xS und yS of the vertex of the parabola are calculated. If the discriminant is equal zero, there is just one solution of the quadratic equation, in the other cases there are two (x1,2 = (-b ±√(b2 - 4ac)) / 2a). If the discriminant is negative, the solutions are complex numbers.

Usage: Type the parameters a, b und c of the quadratic equation into the corresponding fields. If a calculation is possible, this is performed after a click on any empty space of the window or on the "calculate"-button. For cases that you have a quadratic equation in the normalized form x2 + px + q = 0, the value of the parameter a is preset to the value of 1. When you change an input value, the quadratic equation is calculated again.
Input data not valid are deleted before the calculation and are not used.

Example: For the quadatic equation 0.5x2 -5x + 3. = 0 type the parameters a, b, and c into the corresponding fields (a=0.5, b=-5, c=3). After a mouse click on any empty space of the window or on the "calculate"-button the calculation is performed. You receive the result x1=9.5826 and x2=0.41742. The discriminant has a value of 21. Since this is positiv, the solutions are no complex numbers. The parabola of this equation has a vertex at the coordinates xS=5 und yS=-5.25.

Remarks:
- Large and small numbers are written exponentially. As example 2.3e5 = 2.3⋅105 = 230000 or 4.5e-5 = 4.5⋅10-5 = 0.000045.
- There is no warranty for the conversion. Cactus2000 is not responsible for damage of any kind caused by wrong results.
- Please send an email if you have suggestions or if you would like to see more conversions to be included.