Solution calculation of the quartic equation

For example, enter a=3, b=6, c=-123, d=-126 and e=1080 Click to solve the quartic equation \(ax^4 + bx^3 + cx^2 + dx + e = 0\)

quartic equation : ax⁴ + bx³ + cx² + dx + e = 0
Note: Let p and q be the square roots of any two non-zero numbers

root.
p = sqrt(y₁)
q = sqrt(y₃)
r = -g / (8pq)
s = b / (4a)
x₁ = p + q + r - s
x₂ = p - q - r - s
x₃ = -p + q - r - s
x₄ = -p - q + r - s
Cubic equation:
Discriminate(Δ) = q³ + r²
q = (3c- b²)/9
r = -27d + b(9c-2b²)
s = r + math.sqrt(Discriminate)
t = r - math.sqrt(Discriminate)
term1 = math.sqrt(3.0)((-t + s)/2)
r₁₃= 2 * math.sqrt(q)
y₁=(- term1 + r₁₃math.cos(q³/3) )
y₂=(- term1 + r₁₃math.cos(q³+(2math.PI)/3) )
y₃=(- term1 + r₁₃math.cos(q³+(4math.PI)/3) )

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