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Quadratic equations have the form *ax*^{2} + *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.

**Examples for easy calculations:**

Equation: | x1 | x2 |

x^{2} − 2x − 8 = 0 |
4 | −2 |

2x^{2} + 3x − 20 = 0 |
2.5 | −4 |

2x^{2} + 18 = 0 |
0 | −9 |

x^{2} + 5x − 14 = 0 |
2 | −7 |

3x^{2} + 36x − 39 = 0 |
1 | −13 |

9x^{2} − 82x + 9 = 0 |
9 | 1/9 |

8x^{2} + 39x − 5 = 0 |
1/8 | −5 |

6x^{2} − 12x − 6 = 0 |
2.414 | −0.414 |

2.5x^{2} + 17.5x − 20 = 0 |
1 | −8 |

49x^{2} + 154x + 21 = 0 |
−1/7 | −3 |

4x^{2} + (107/3)x − 3 = 0 |
1/12 | −9 |

2x^{2} − 20.8x + 8 = 0 |
10 | 2/5 |

12x^{2} + x − 1 = 0 |
− 1/4 | 1/3 |

3x^{2} + 9x − 12 = 0 |
1 | −4 |

5x^{2} − 2x − 3/5 = 0 |
3/5 | −1/5 |

x^{2} − 0.9x + 0.7 = 0 |
1.4 | − 0.5 |

5x^{2} − 16.5x + 13 = 0 |
−1.3 | −2 |

0.5x^{2} − 8x + 32 = 0 |
8 | 8 |

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