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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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