Solving x with a*b*c^3, Pie^2, i & 16

[arslan894]

w=a*b*c^3*x*√(pie^2 * (i-x^2)^2 + 16 *x^2)/ 4*d^2 *(1-x^2)^2 I have to find x ,i have the values of all other constants ,
I tried to separate it using partial fraction but I am stuck.

 

[HallsofIvy]

Tedious but,
1) multiply both sides by that denominator:
$$4wd^3(1- x^2)= abc^3x\sqrt{\pi^2(i- x^2)+ 16x^2}$$

2) get rid of that square root by squaring both sides:
$$16w^2d^y(1- 2x^2+ x^4)= a^2b^2c^6x^2(\pi(I- x^2)+ 16x^2)$$

That is now a fourth degree polynomial- there is a general "formula" for solving such polynomial equations but it is very complicated.