solve 2x+1=√(6x+2x^2+5)

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I assume that is a square root sign. Square both sides (use FOIL): 4x^2 + 4x + 1 = 2x^2 + 6x + 5 Combine like terms and write in standard form: 2x^2 - 2x - 4 = 0  same as  x^2 - x - 2 = 0 Factor into:  (x - 2)(x + 1) = 0 Solution:  x = 2 or x = -1