# Solve equation with inequalities for parameters

I want to solve following equation:

Solve[{g^2 - gamma*alpha + alpha^2 -
omega*(omega*alpha)/(gamma - 2*alpha) - (omega^2*
alpha^2)/(gamma - 2*alpha)^2 == 0, gamma > 0, omega > 0,
g > 0}, alpha]


I want to become an analytic, explicit expression for alpha, but Mathematica gives me only a solution with Root; for example, (there are more solutions):

{alpha ->
ConditionalExpression[
I Root[g^2 gamma^2 -
4 g^2 gamma Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1] -
gamma^3 Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1] -
gamma omega^2 Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1] +
4 g^2 Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1]^2 +
5 gamma^2 Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1]^2 +
omega^2 Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1]^2 -
8 gamma Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1]^3 +
4 Root[g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &,
1]^4 + (-4 g^2 - 5 gamma^2 - omega^2 +
24 gamma Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &, 1] -
24 Root[
g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 +
omega^2) #1^2 - 8 gamma #1^3 + 4 #1^4 &,
1]^2) #1^2 + 4 #1^4 &, 2] +
Root[g^2 gamma^2 + (-4 g^2 gamma - gamma^3 -
gamma omega^2) #1 + (4 g^2 + 5 gamma^2 + omega^2) #1^2 -
8 gamma #1^3 + 4 #1^4 &, 1], g > 0 && gamma > 0 && omega > 0]}


This is not an explicit solution. I have also tried Reduce without success.

What can I do?

-
As a response indicates, you can just convert the Root functions into radicals. But actually the Root things themselves are explicit, and for many purposes they are better behaved than parametrized radicals. – Daniel Lichtblau Feb 26 '13 at 14:23

Solve[{g^2 - gamma alpha + alpha^2 - (omega (omega alpha))/(