Nim equations

See problem 307 on Nim operations. Find the 2 roots of the following equations where Nim operations are used only: 1881x² + 1923x + 1938 = 0 where roots: x₁ < 2¹³ < x₂ 6273x² + 2935220086x + 2831770815 = 0 where roots: x₃ < 2¹⁶ < x₄ 6273x² + 12997147727796204837x + 11460394964710426743 = 0 where roots: x₅ < 2²⁴ < x₆ Answer format: x₁,x₂,x₃,x₄,x₅,x₆ [My timing: <15s]