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Solve[(u (Sqrt[8 p] - 3 Sqrt[u])^2 (Sqrt[8 p] Sqrt[u] - 2 p - 3 u))/(
   2 (Sqrt[u] - Sqrt[8 p])^2) + (2 p)/3 == 0, u]
Natas
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Qutubu
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1 Answers1

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All you have to do is pick a value for p and the Root goes away.

sol = Solve[(u (Sqrt[8 p] - 3 Sqrt[u])^2 (Sqrt[8 p] Sqrt[u] - 2 p - 3 u))/(2 (Sqrt[u] - Sqrt[8 p])^2) + (2 p)/3 == 0, u]

sol /. p -> .1


{{u -> 0.0842808}, {u -> 
   0.217977}, {u -> -0.144139 - 0.00221632 I}, {u -> -0.144139 + 
    0.00221632 I}, {u -> 0.0596765 - 0.193184 I}, {u -> 
   0.0596765 + 0.193184 I}}
Bill Watts
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  • Thanks @Bill watts, but whenever I pick p=100 then root still there. – Qutubu Aug 28 '20 at 08:32
  • Try 100. Instead of an integer, or add //N. – Bill Watts Aug 28 '20 at 08:43
  • @Qutubu - With an exact input (100), you get an exact result (the Root expression). As @BillWatts indicated, to get an approximate result use an inexact input or use N to convert the exact solution (Root) to its approximate value. – Bob Hanlon Aug 28 '20 at 18:35