(7/x)+(-6/x-5)=(-31)/(x2-5x)

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Solution for (7/x)+(-6/x-5)=(-31)/(x2-5x) equation: 


D( x )

x = 0

x^2-(5*x) = 0

x = 0

x = 0

x^2-(5*x) = 0

x^2-(5*x) = 0

x^2-5*x = 0

x^2-5*x = 0

DELTA = (-5)^2-(0*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+5)/(1*2) or x = (5-25^(1/2))/(1*2)

x = 5 or x = 0

x in (-oo:0) U (0:5) U (5:+oo)

7/x-6/x-5 = -31/(x^2-(5*x)) // + -31/(x^2-(5*x))

7/x-(-31/(x^2-(5*x)))-6/x-5 = 0

31*(x^2-5*x)^-1+7/x-6/x-5 = 0

31/(x^2-5*x)+7/x-6/x-5 = 0

x^2-5*x = 0

x^2-5*x = 0

x*(x-5) = 0

x-5 = 0 // + 5

x = 5

x*(x-5) = 0

31/(x*(x-5))+7/x-6/x-5 = 0

31/(x*(x-5))+(7*(x-5))/(x*(x-5))+(-6*(x-5))/(x*(x-5))+(-5*x*(x-5))/(x*(x-5)) = 0

7*(x-5)-6*(x-5)-5*x*(x-5)+31 = 0

7*x-5*x^2-6*x+25*x-4+30 = 0

x-5*x^2+25*x+26 = 0

26*x-5*x^2+26 = 0

26*x-5*x^2+26 = 0

26*x-5*x^2+26 = 0

DELTA = 26^2-(-5*4*26)

DELTA = 1196

DELTA > 0

x = (1196^(1/2)-26)/(-5*2) or x = (-1196^(1/2)-26)/(-5*2)

x = (2*299^(1/2)-26)/(-10) or x = (-2*299^(1/2)-26)/(-10)

(x-((2*299^(1/2)-26)/(-10)))*(x-((-2*299^(1/2)-26)/(-10))) = 0

((x-((2*299^(1/2)-26)/(-10)))*(x-((-2*299^(1/2)-26)/(-10))))/(x*(x-5)) = 0

((x-((2*299^(1/2)-26)/(-10)))*(x-((-2*299^(1/2)-26)/(-10))))/(x*(x-5)) = 0 // * x*(x-5)

(x-((2*299^(1/2)-26)/(-10)))*(x-((-2*299^(1/2)-26)/(-10))) = 0

( x-((-2*299^(1/2)-26)/(-10)) )

x-((-2*299^(1/2)-26)/(-10)) = 0 // + (-2*299^(1/2)-26)/(-10)

x = (-2*299^(1/2)-26)/(-10)

( x-((2*299^(1/2)-26)/(-10)) )

x-((2*299^(1/2)-26)/(-10)) = 0 // + (2*299^(1/2)-26)/(-10)

x = (2*299^(1/2)-26)/(-10)

x in { (-2*299^(1/2)-26)/(-10), (2*299^(1/2)-26)/(-10) }

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