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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

$({-g+\sqrt {g^2/4+f^3/27} })^{1/3} + ({-g-\sqrt {g^2/4+f^3/27} })^{1/3}$

$-\frac{f}{3 (-\frac{1}{2}g + \frac{1}{6} \sqrt{\frac{4}{3}f^3+9g^2}) ^{1/3} } == ({-g+\sqrt {g^2/4+f^3/27} })^{1/3}$

How do I check

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

$({-g+\sqrt {g^2/4+f^3/27} })^{1/3} + ({-g-\sqrt {g^2/4+f^3/27} })^{1/3}$

$-\frac{f}{3 (-\frac{1}{2}g + \frac{1}{6} \sqrt{\frac{4}{3}f^3+9g^2}) ^{1/3} } == ({-g+\sqrt {g^2/4+f^3/27} })^{1/3}$

How do I checkcheck. I want to use sage,not math. In particular the bool() function.