Question

If -nx^3 + tx + c = 0, what is x equal to?


Never mind, found it. 

Answer 1

`-nx^3 + tx + c = 0\ /:(-n)\ \ \ \wedge\ \ \ n \\eq 0\\ \\x^3- (t)/(n) x-(c)/(n)=0\\ \\\Delta=(- (t)/(n))^3+(-(c)/(n))^2= (-t^3)/(n^3) + (c^2)/(n^2) = (-t^3+n\cdot c^2)/(n^3) \\ \\\Delta>0\ \ \Rightarrow\ \ \ x= \sqrt[3]{ (c)/(2n)- \sqrt\Delta} } +\sqrt[3]{ (c)/(2n)+ \sqrt\Delta} \\ \\\Delta=0\ \ \ \Rightarrow\ \ \ x_1=\sqrt[3]{ (c)/(2n)},\ \ \ \ x_2=-2\sqrt[3]{ (c)/(2n)}\\ \\\Delta<0\ \ \ \Rightarrow\ \ \ there\ is\ no\ solution\ for\ x\in R`