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We will solve (for X) the polynomial of the form:

aX^{3} + bX^{2} + cX + d = 0.

First input the rational coefficients for a, b, c, d.

(Click 'Next' when you're finished)

Next

aX

First input the rational coefficients for a, b, c, d.

(Click 'Next' when you're finished)

Next

By dividing the coefficients by the value of 'a' we get,
Next

We now transform the cubic by making the substitution Y=X+b/3 to put the polynomial in the form of Y^{3}+pY+q = 0. Giving us

Next

Next

We can now calculate the discriminant
D = q^{2}/4 + p^{3}/27
or
Next

We can now calculate the real root of Y^{3}+pY+q = 0 by

thus

thus

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