(5-x)/(10x-x^2)^0.5

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Solution for (5-x)/(10x-x^2)^0.5 equation: 


D( x )

10*x-x^2 < 0

(10*x-x^2)^0.5 = 0

10*x-x^2 < 0

10*x-x^2 < 0

10*x-x^2 < 0

DELTA = 10^2-(-1*0*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)-10)/(-1*2) or x = (-100^(1/2)-10)/(-1*2)

x = 0 or x = 10

a = -1

a < 0

x in (-oo:0) U (10:+oo)

(10*x-x^2)^0.5 = 0

(10*x-x^2)^0.5 = 0

10*x-x^2 = 0

x*(10-x) = 0

10-x = 0 // - 10

-x = -10 // * -1

x = 10

x*(x-10) = 0

x^0.5*(x-10)^0.5 = 0

( x-10 )

x-10 = 0 // + 10

x = 10

( x )

x = 0

x in (0:10)

(5-x)/((10*x-x^2)^0.5) = 0

10*x-x^2 = 0

x*(10-x) = 0

10-x = 0 // - 10

-x = -10 // * -1

x = 10

x*(x-10) = 0

(5-x)/(x^0.5*(x-10)^0.5) = 0

5-x = 0 // - 5

-x = -5 // * -1

x = 5

x = 5

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