I'm failing to solve a cubic equation
Solution 1:
When you depress a cubic, you make the substitution $t = x+b/3a$. For your example that would be $t = x+3/(2\cdot 3) =x + 1/2$.
You're using $x$ in two ways. In your depressed equation, the $x$ should be a different variable, say $t$. You're getting $-0.8711$ for $t$. But $t=x+1/2$, so....