I'm trying to solve a more complex cubic equation but to simplify things as a start I picked this one:
$$ 3\cdot 4^3+2\cdot 4-200=0 $$
Here $x$ is $4$.
I'm looking at wikipedia and trying to solve with the general cubic formula.
In my case I have
$$ a = 3, b = 1, c = 2, d = -200 $$
So solving for $\Delta_0$
$$ \Delta_0 = b^2 - 3ac $$ $$ \Delta_0 = 1^2 - 3\cdot3\cdot2 $$ $$ \Delta_0 = -17 $$
Solving for $\Delta_1$
$$ \Delta_1 = 2b^3 - 9abc + 27a^2d $$ $$ \Delta_1 = 2\cdot1^3 - 9\cdot3\cdot1\cdot2 + 27\cdot3^2\cdot-200 $$ $$ \Delta_1 = −48652 $$
At this point already I feel like something is wrong.
I kept going and got some very negative numbers for the rest, which are obviously not correct, so I'll spare you the details.
What am I doing wrong?