The standard cubic equation aX^3+bX^2+cX+d=0 (a, b, c, d∈R, and a≠0) has two solutions: 1. Cardan's formula published by Italian scholar Cardan in 1545; 2. Shengjin's formula published by Chinese scholar Fan Shengjin in 1989.

Both formulas can solve standard cubic equations. Since the Cardan formula is complex to solve, the Shengjin formula is concise, clear, easy to remember, and more intuitive and efficient in solving problems.

Shengjin formula discrimination method

When A=B=0, the equation has a triple real root.

When Δ=B^2－4AC>0, the equation has one real root and a pair of conjugate imaginary roots.

When Δ=B^2-4AC=0, the equation has three real roots, one of which is a double root.

When Δ=B^2－4AC<0, the equation has three unequal real roots.