How can I rearrange the equation x = y(1-z)/π√z to solve for z?

[totty3478]

Hi,

I have recently returned to education after 15 years out and I am finding that it is my basic maths that causes me the most problems. I have the following equation

x = y (1-z)/ $$\pi$$ $$\sqrt{}z$$

so you know, that's pi multiplied by root z.

and I can't solve for z, can someone rearrange this equation for me.

thanks

 

[HallsofIvy]

Do you mean
[tex]x= \ffrac{y(1-z)}{\pi\sqrt{z}}[/itex]?
That would be the same as $\pi x\sqrt{z}= y- yz$ or [itex]yz+ \pi x\sqrt{z}- y= 0[itex].

Let $u= \sqrt{z}$ so that $u^2= z$. Then the equation becomes $yu^2+ \pi xu+ y= 0$, a quadratic equation for u. That can be solved using the quadratic formula and then square u to find z.

 

[NoMoreExams]

To me that kind of looked like:

$$x = \frac{y(1-z)}{\sqrt[\pi]{z}}$$

But it could be anything.

 

[totty3478]

sorry I will try again, the equation should be

$$x = \frac{y(1-z)}{\pi\sqrt{z}}$$

then solve for z

thanks

 

[tim_lou]

substitute $$z'=\sqrt{z}$$ and you get a quadratic eq.. Then multiply both sides by $\pi z'$

 

[totty3478]

Thanks guys, I got the answer i was looking for after I made it into a quadratic.

Thanks for your help