C#盛金公式求解一元三次方程

static float A;
        static float B;
        static float C;
        static float delta;
        static float x1, x2, x3;
        static float x2_real, x3_real, x2_virtual, x3_virtual;
        static float deltaQuadratic;

        /// <summary>
        /// 盛金公式求解一元三次方程
        /// </summary>
        /// <param name="a">三次系数</param>
        /// <param name="b">二次系数</param>
        /// <param name="c">一次系数</param>
        /// <param name="d">常系数</param>
        /// <param name="r1">结果1 为null则没有实根</param>
        /// <param name="r2">结果2</param>
        /// <param name="r3">结果3</param>
        private static void solveEquations(float a, float b, float c, float d, out float r1, out float r2, out float r3)
        {
            r1 = 0;
            r2 = 0;
            r3 = 0;

            A = b * b - 3 * a * c;
            B = b * c - 9 * a * d;
            C = c * c - 3 * b * d;
            delta = B * B - 4 * A * C;

            if (d == 0)
            {
                x3 = 0;
                solveQuadraticEquation(a, b, c, d);
            }
            else if (A == 0 && B == 0)
            {
                x1 = -b / (3 * a);
                x2 = -c / b;
                x3 = -3 * d / c;

            }
            else if (delta > 0)
            {
                float Y1 = float.Parse((A * b + 3 * a * (-B + Math.Sqrt(delta)) / 2).ToString());
                float Y2 = float.Parse((A * b + 3 * a * (-B - Math.Sqrt(delta)) / 2).ToString());

                x1 = (-b - (getCubeRoot(Y1) + getCubeRoot(Y2))) / (3 * a);
                x3_real = x2_real = (-b + getCubeRoot(Y1)) / (3 * a);
                x2_virtual = float.Parse((((Math.Sqrt(3) / 2) * (getCubeRoot(Y1) - getCubeRoot(Y2))) / (3 * a)).ToString());
                x3_virtual = -x2_virtual;
            }
            else if (delta == 0)
            {
                var K = B / A; //A != 0
                x1 = -b / a + K;
                x2 = x3 = -K / 2;
            }
            else
            {
                //delta < 0
                var T = (2 * A * b - 3 * a * B) / (2 * Math.Sqrt(A * A * A)); // A > 0, -1 < T < 1
                var angle = Math.Acos(T) / 3;
                x1 = float.Parse(((-b - 2 * Math.Sqrt(A) * Math.Cos(angle)) / (3 * a)).ToString());
                x2 = float.Parse(((-b + Math.Sqrt(A) * (Math.Cos(angle) + Math.Sqrt(3) * Math.Sin(angle))) / (3 * a)).ToString());
                x3 = float.Parse(((-b + Math.Sqrt(A) * (Math.Cos(angle) - Math.Sqrt(3) * Math.Sin(angle))) / (3 * a)).ToString());
            }

            if (A == 0 && B == 0)
            {
                //方程有一个三重实根
                r1 = x1;
                r2 = x1;
                r3 = x1;
                return;
            }
            else if (delta > 0)
            {
                //方程有一个实根和一对共轭虚根
                r1 = x1;
                r2 = x2_real + x2_virtual;
                r3 = x2_real + x2_virtual;
            }
            else if (delta == 0)
            {
                //方程有一个实根，其中有一个两重根
                r1 = x1;
                r2 = x2;
                r3 = x2;
            }
            else
            {
                //方程有三个不相等的实根
                r1 = x1;
                r2 = x2;
                r3 = x3;
            }
        }

        private static void solveQuadraticEquation(float a, float b, float c, float d)
        {
            deltaQuadratic = b * b - 4 * a * c;
            if (deltaQuadratic == 0)
            {
                x1 = x2 = -b / (2 * a);
            }
            else if (deltaQuadratic > 0)
            {
                x1 = -b + float.Parse((Math.Sqrt(deltaQuadratic) / (2 * a)).ToString());
                x2 = -b - float.Parse((Math.Sqrt(deltaQuadratic) / (2 * a)).ToString());
            }
            else
            {
                x2_real = -b / (2 * a);
                x2_virtual = float.Parse((Math.Sqrt(-deltaQuadratic) / (2 * a)).ToString());
            }
        }

        private static float getCubeRoot(float value)
        {
            if (value < 0)
            {
                return float.Parse((-Math.Pow(-value, 1 / 3)).ToString());
            }
            else if (value == 0)
            {
                return 0;
            }
            else
            {
                return float.Parse(Math.Pow(value, 1 / 3).ToString());
            }
        }

调用solveEquations方法即可。