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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(-1/2)*x+4+10 = 5/x+5 // - 5/x+5
(-1/2)*x-(5/x)-5+4+10 = 0
(-1/2)*x-5*x^-1-5+4+10 = 0
9*x^0-1/2*x^1-5*x^-1 = 0
(9*x^1-1/2*x^2-5*x^0)/(x^1) = 0 // * x^2
x^1*(9*x^1-1/2*x^2-5*x^0) = 0
x^1
(-1/2)*x^2+9*x-5 = 0
(-1/2)*x^2+9*x-5 = 0
DELTA = 9^2-(-5*4*(-1/2))
DELTA = 71
DELTA > 0
x = (71^(1/2)-9)/(2*(-1/2)) or x = (-71^(1/2)-9)/(2*(-1/2))
x = 9-71^(1/2) or x = 71^(1/2)+9
x in { 9-71^(1/2), 71^(1/2)+9}
x in { 9-71^(1/2), 71^(1/2)+9 }
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