Methods to find solutions to an equation of form $A=BT^{1.5} + CT^{2.5}$

Question

As the title goes, I have arrived at an equation of the form:

$$A=BT^{\frac{3}{2}}+CT^{\frac{5}{2}}$$

Where A,B and C are known constants.

How do you go about finding possible solutions for T?

Answer 1

You can define $S:=\sqrt{T}$ thus arriving at a polynomial equation $CS^5+BS^3=S^3(CS^2+B)=A$, which can be treated numerically using Newton's method.