2x-1/x=4/3

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Solution for 2x-1/x=4/3 equation: 


D( x )

x = 0

x = 0

x = 0

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

2*x-(1/x) = 4/3 // - 4/3

2*x-(1/x)-(4/3) = 0

2*x-x^-1-4/3 = 0

2*x^1-1*x^-1-4/3*x^0 = 0

(2*x^2-4/3*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^2-4/3*x^1-1*x^0) = 0

x^1

2*x^2+(-4/3)*x-1 = 0

2*x^2+(-4/3)*x-1 = 0

DELTA = (-4/3)^2-(-1*2*4)

DELTA = 88/9

DELTA > 0

x = ((88/9)^(1/2)-(-4/3))/(2*2) or x = (-(-4/3)-(88/9)^(1/2))/(2*2)

x = ((88/9)^(1/2)+4/3)/4 or x = (4/3-(88/9)^(1/2))/4

x in { (4/3-(88/9)^(1/2))/4, ((88/9)^(1/2)+4/3)/4} 

x in { (4/3-(88/9)^(1/2))/4, ((88/9)^(1/2)+4/3)/4 }

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