a=

b=

c=

L h

L k

L u

Root β

Root γ

a=

b=

c=

Lp

Lu_1

Lu_2

α

Omega

β

γ

L w

=B2² + 4B1³.

If B15 is greater than 0, B16, B17.

Calculation α+β+γ

Root α

Calculation αβ + αγ + βγ

Calculation αβγ

=-Coefficient a

=Coefficient b

=-Coefficient c

cubic(a, b, c, x) = x^(3) + a * x^(2) + b * x + c
h(a, b) = (3 * b - a^(2)) / 9
k(a, b, c) = (2 * a^(3) - 9 * a * b + 27 * c) / 27
u(k, h) = (0.5 * (-k + (k^(2) + 4 * h^(3))^(0.5)))^(1 / 3)
w = (-0.5, 0.8660254037844386)
α(a, h, u) = u - h / u - a / 3
β(a, h, u, w) = u * w - (h * w^(2)) / u - a / 3
γ(a, h, u, w) = u * w^(2) - (h * w) / u - a / 3
a = 4 (slider from -100 to 100, step 0.01)
b = -6 (slider from -100 to 100, step 0.01)
c = -40 (slider from -100 to 100, step 0.01)
z: α
B2: (2 * a^(3) - 9 * a * b + 27 * c) / 27
A2: k
B1: (3 * b - a^(2)) / 9
A3: u
A1: h
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c)
B15: B2^(2) + 4 * B1^(3)
B16: (0.5 * (-B2 + sqrt(abs(B15))))^(1 / 3) + 0 * ί
e: abs(B15^(0.5))
B17: (0.5 * (-B2 + ί * abs(B15)^(0.5)))^(1 / 3)
B18 = If(B15 ≥ 0, B16, B17)
B3: B18
B6: B3 - B1 / B3 - a / 3
B5 = (-0.5, 0.8660254037844386)
B7: B3 * B5 - (B1 * B5^(2)) / B3 - a / 3
B8: B3 * B5^(2) - (B1 * B5) / B3 - a / 3
poly1, b5, b6, b7 = Polygon(B7, B8, B6)
d = Circle(B6, B7, B8)
B10: B6 + B7 + B8
B11: B6 * B7 + B6 * B8 + B7 * B8
B12: B6 * B7 * B8