>>> from quadratic import real_roots

(x-1)(x-3) = x²-4x+3

>>> a, b, c = 1, -4, 3
>>> x1, x2 = real_roots(a, b, c)
>>> a*x1**2+b*x1+c == 0
True
>>> a*x2**2+b*x2+c == 0
True

(x+1)(x-3) = x²-2x-3

>>> a, b, c = 1, -2, -3
>>> x1, x2 = real_roots(a, b, c)
>>> a*x1**2+b*x1+c == 0
True
>>> a*x2**2+b*x2+c == 0
True

(x-2)(x-2) = x²-4x+4

>>> a, b, c = 1, -4, 4
>>> x1, x2 = real_roots(a, b, c)
>>> a*x1**2+b*x1+c == 0
True
>>> a*x2**2+b*x2+c == 0
True

(x+1/2)(x-2) = 2x²-3x-2

>>> a, b, c = 2, -3, -2
>>> x1, x2 = real_roots(a, b, c)
>>> a*x1**2+b*x1+c == 0
True
>>> a*x2**2+b*x2+c == 0
True

(x+1)(x-2/3) = 3x²+1x-2

>>> a, b, c = 3, 1, -2
>>> x1, x2 = real_roots(a, b, c)
>>> a*x1**2+b*x1+c == 0
True
>>> a*x2**2+b*x2+c == 0
True