2/3x+5/6=7/(6x)

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Solution for 2/3x+5/6=7/(6x) equation:


D( x )

6*x = 0

6*x = 0

6*x = 0

6*x = 0 // : 6

x = 0

x in (-oo:0) U (0:+oo)

(2/3)*x+5/6 = 7/(6*x) // - 7/(6*x)

(2/3)*x-(7/(6*x))+5/6 = 0

(2/3)*x+(-7/6)*x^-1+5/6 = 0

2/3*x^1-7/6*x^-1+5/6*x^0 = 0

(2/3*x^2+5/6*x^1-7/6*x^0)/(x^1) = 0 // * x^2

x^1*(2/3*x^2+5/6*x^1-7/6*x^0) = 0

x^1

(2/3)*x^2+(5/6)*x-7/6 = 0

(2/3)*x^2+(5/6)*x-7/6 = 0

DELTA = (5/6)^2-(4*(2/3)*(-7/6))

DELTA = 137/36

DELTA > 0

x = ((137/36)^(1/2)-(5/6))/(2*(2/3)) or x = (-(5/6)-(137/36)^(1/2))/(2*(2/3))

x = 3/4*((137/36)^(1/2)-5/6) or x = -3/4*((137/36)^(1/2)+5/6)

x in { -3/4*((137/36)^(1/2)+5/6), 3/4*((137/36)^(1/2)-5/6)}

x in { -3/4*((137/36)^(1/2)+5/6), 3/4*((137/36)^(1/2)-5/6) }

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