Code:

import sympy

k = sympy.symbols('k')
x = sympy.symbols('x')

# Equation: kx(x-2) + 6 = 0
expr = k*x*(x-2) + 6
poly = sympy.Poly(expr, x)
coeffs = poly.coeffs()
a = coeffs[0]
b = coeffs[1]
c = coeffs[2]

# Discriminant D = b^2 - 4ac
discriminant = b**2 - 4*a*c
solutions = sympy.solve(discriminant, k)

# Filter solutions: k cannot be 0 because it's a quadratic equation
valid_solutions = [sol for sol in solutions if sol != 0]

print(f"{a=}")
print(f"{b=}")
print(f"{c=}")
print(f"{discriminant=}")
print(f"{solutions=}")
print(f"{valid_solutions=}")

Output:

a=k
b=-2*k
c=6
discriminant=4*k**2 - 24*k
solutions=[0, 6]
valid_solutions=[6]