How to re-arrange this quadratic equation

[pedro39]

Can anyone let me know how to arrange the formula below to calculate for V please?

 

[lev888]

"Quadratic equation - Wikipedia" https://en.m.wikipedia.org/wiki/Quadratic_equation

 

[Dr.Peterson]

Can anyone let me know how to arrange the formula below to calculate for V please?

View attachment 26847

Just subtract the LHS to put it in the form aV^2 + bV + c = 0, and then use the quadratic formula. The coefficients are easy to see.

I would first clear fractions, by multiplying by the LCD.

 

[pedro39]

Thanks for your help. I've now worked it out. Much appreciated.

 

[JeffM]

Can anyone let me know how to arrange the formula below to calculate for V please?

View attachment 26847

Just substitute variables after clearing the denominator of the coefficient of V.

[MATH]\dfrac{\Delta P}{L} = 150 * \dfrac{\mu_fV(1 - e)^2}{\phi_s^2D_p^2e^3} + 1.75 * \dfrac{\rho_fV^2(1 - e)}{\phi_sD_pe^3} \implies[/MATH]
[MATH]\dfrac{\Delta P}{L} * \dfrac{\phi_sD_pe^3}{(1 - e)} = \dfrac{150\mu_fV(1 - e)}{\phi_sD_p} + 1.75 \rho_fV^2.[/MATH]
[MATH]\text {Let } \gamma = \dfrac{\Delta P}{L} * \dfrac{\phi_sD_pe^3}{(1 - e)}, \ \beta = \dfrac{150\mu_f(1 - e)}{\phi_sD_p},[/MATH]
[MATH]\text { and } \alpha = 1.75 \rho_f.[/MATH]
[MATH]\therefore \gamma = \beta V + \alpha V^2 \implies V = \dfrac{- \beta \pm \sqrt{\beta^2 + 4 \alpha \gamma}}{2 \alpha}.[/MATH]
In all probability, the negative value is meaningless.