5/9x+18=5/x+2-4/9

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Solution for 5/9x+18=5/x+2-4/9 equation:


D( x )

x = 0

x = 0

x = 0

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

(5/9)*x+18 = 5/x-(4/9)+2 // - 5/x-(4/9)+2

(5/9)*x-(5/x)+4/9-2+18 = 0

(5/9)*x-5*x^-1+4/9-2+18 = 0

5/9*x^1-5*x^-1+148/9*x^0 = 0

(5/9*x^2+148/9*x^1-5*x^0)/(x^1) = 0 // * x^2

x^1*(5/9*x^2+148/9*x^1-5*x^0) = 0

x^1

(5/9)*x^2+(148/9)*x-5 = 0

(5/9)*x^2+(148/9)*x-5 = 0

DELTA = (148/9)^2-(-5*4*(5/9))

DELTA = 22804/81

DELTA > 0

x = ((22804/81)^(1/2)-(148/9))/(2*(5/9)) or x = (-(148/9)-(22804/81)^(1/2))/(2*(5/9))

x = 9/10*((22804/81)^(1/2)-148/9) or x = -9/10*((22804/81)^(1/2)+148/9)

x in { -9/10*((22804/81)^(1/2)+148/9), 9/10*((22804/81)^(1/2)-148/9)}

x in { -9/10*((22804/81)^(1/2)+148/9), 9/10*((22804/81)^(1/2)-148/9) }

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