 step 1 in solving x6x+30 for x   The cubic is x + px+qx6x+3, so p6 and q3.   The discriminant is 4p27q = 621 > 0, so there are three real roots and we can   We wish to find the three real solutions to x6x+30.   First, compute the number ϕ.   As the discriminant is positive, 1≤ϕ≤1, and therefore ϕ is the cosine of some angle 

 

