6/9x+45=7/x+5-4/9

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Solution for 6/9x+45=7/x+5-4/9 equation:


D( x )

x = 0

x = 0

x = 0

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

(6/9)*x+45 = 7/x-(4/9)+5 // - 7/x-(4/9)+5

(6/9)*x-(7/x)+4/9-5+45 = 0

(6/9)*x-7*x^-1+4/9-5+45 = 0

2/3*x^1-7*x^-1+364/9*x^0 = 0

(2/3*x^2+364/9*x^1-7*x^0)/(x^1) = 0 // * x^2

x^1*(2/3*x^2+364/9*x^1-7*x^0) = 0

x^1

(2/3)*x^2+(364/9)*x-7 = 0

(2/3)*x^2+(364/9)*x-7 = 0

DELTA = (364/9)^2-(-7*4*(2/3))

DELTA = 134008/81

DELTA > 0

x = ((134008/81)^(1/2)-(364/9))/(2*(2/3)) or x = (-(364/9)-(134008/81)^(1/2))/(2*(2/3))

x = 3/4*((134008/81)^(1/2)-364/9) or x = -3/4*((134008/81)^(1/2)+364/9)

x in { -3/4*((134008/81)^(1/2)+364/9), 3/4*((134008/81)^(1/2)-364/9)}

x in { -3/4*((134008/81)^(1/2)+364/9), 3/4*((134008/81)^(1/2)-364/9) }

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