3x-5/x10

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Solution for 3x-5/x10 equation:


D( x )

x = 0

x = 0

x = 0

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

3*x-(5/x) > 10 // - 10

3*x-(5/x)-10 > 0

3*x-5*x^-1-10 > 0

3*x-5*x^-1-10 = 0

3*x^1-5*x^-1-10*x^0 = 0

(3*x^2-10*x^1-5*x^0)/(x^1) = 0 // * x^2

x^1*(3*x^2-10*x^1-5*x^0) = 0

x^1

3*x^2-10*x-5 = 0

3*x^2-10*x-5 = 0

DELTA = (-10)^2-(-5*3*4)

DELTA = 160

DELTA > 0

x = (160^(1/2)+10)/(2*3) or x = (10-160^(1/2))/(2*3)

x = (4*10^(1/2)+10)/6 or x = (10-4*10^(1/2))/6

x in { (10-4*10^(1/2))/6, (4*10^(1/2)+10)/6}

(x-((10-4*10^(1/2))/6))*(x-((4*10^(1/2)+10)/6)) > 0

(-oo:(10-4*10^(1/2))/6) ((10-4*10^(1/2))/6:(4*10^(1/2)+10)/6) ((4*10^(1/2)+10)/6:+oo) x-((10-4*10^(1/2))/6) - + + x-((4*10^(1/2)+10)/6) - - +

x in (-oo:(10-4*10^(1/2))/6) U ((4*10^(1/2)+10)/6:+oo)

(-oo:(10-4*10^(1/2))/6) U ((4*10^(1/2)+10)/6:+oo)

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