# Math Help - Solve y(x)=sqrt(x)*(A+B*x)-C=0 ?

1. ## Solve y(x)=sqrt(x)*(A+B*x)-C=0 ?

Hello everyone, I just came along the following function:

y(x) = sqrt(x)*(A+B*x)-C=0

x is the independent variable and A,B,C are constant numbers.

How can we solve this function for x? Is it possible analytically?

Daniel

2. Originally Posted by dbecker
Hello everyone, I just came along the following function:

y(x) = sqrt(x)*(A+B*x)-C=0

x is the independent variable and A,B,C are constant numbers.

How can we solve this function for x? Is it possible analytically?

Daniel
With the substitution $\alpha= \sqrt{x}$ the equation becomes...

$b\ \alpha^{3} + a\ \alpha -c=0$ (1)

... the algebraic solution of which was found in Italy in the XVI-th century ...

Kind regards

$\chi$ $\sigma$

3. Thank you! Now it's just obvious

Regards,
Daniel