The quadratic formula

When a quadratic does not factorise, use the formula. For ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a. The ± gives two answers, one with + and one with −.

For x² − 6x + 6 = 0, a = 1, b = −6 and c = 6. Then b² − 4ac = 36 − 24 = 12, so x = (6 ± √12)/2, which gives x = 4.73 or 1.27 to 2 decimal places. The part b² − 4ac, the discriminant, tells you how many solutions there are: two if it is positive, one if zero and none if negative.