(8/3x)-(2/x)=(5/6)

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Solution for (8/3x)-(2/x)=(5/6) equation: 


D( x )

x = 0

x = 0

x = 0

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

(8/3)*x-(2/x) = 5/6 // - 5/6

(8/3)*x-(2/x)-(5/6) = 0

(8/3)*x-2*x^-1-5/6 = 0

8/3*x^1-2*x^-1-5/6*x^0 = 0

(8/3*x^2-5/6*x^1-2*x^0)/(x^1) = 0 // * x^2

x^1*(8/3*x^2-5/6*x^1-2*x^0) = 0

x^1

(8/3)*x^2+(-5/6)*x-2 = 0

(8/3)*x^2+(-5/6)*x-2 = 0

DELTA = (-5/6)^2-(-2*4*(8/3))

DELTA = 793/36

DELTA > 0

x = ((793/36)^(1/2)-(-5/6))/(2*(8/3)) or x = (-(-5/6)-(793/36)^(1/2))/(2*(8/3))

x = 3/16*((793/36)^(1/2)+5/6) or x = 3/16*(5/6-(793/36)^(1/2))

x in { 3/16*(5/6-(793/36)^(1/2)), 3/16*((793/36)^(1/2)+5/6)} 

x in { 3/16*(5/6-(793/36)^(1/2)), 3/16*((793/36)^(1/2)+5/6) }

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