So, i got a different cubic formula for the depressed equation than that was there in the standard formula from a book. $y^3+fy+g=0 $ has the solution
$ ({-g+\sqrt {g^2/4-f} })^{1/3} + ({-g-\sqrt {g^2/4-f} })^{1/3} $
$ \left{y : -\frac{f}{3 \, {\left(-\frac{1}{2} \, g + \frac{1}{6} \, \sqrt{\frac{4}{3} \, f^{3} + 9 \, g^{2}}\right)}^{\frac{1}{3}}} + {\left(-\frac{1}{2} \, g + \frac{1}{6} \, \sqrt{\frac{4}{3} \, f^{3} + 9 \, g^{2}}\right)}^{\frac{1}{3}}\right} $