8/(x-5)-x=-1

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Solution for 8/(x-5)-x=-1 equation: 


D( x )

x-5 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

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

8/(x-5)-x = -1 // + 1

8/(x-5)-x+1 = 0

8/(x-5)+(-x*(x-5))/(x-5)+(1*(x-5))/(x-5) = 0

1*(x-5)-x*(x-5)+8 = 0

5*x-x^2+x-5+8 = 0

6*x-x^2+3 = 0

6*x-x^2+3 = 0

6*x-x^2+3 = 0

DELTA = 6^2-(-1*3*4)

DELTA = 48

DELTA > 0

x = (48^(1/2)-6)/(-1*2) or x = (-48^(1/2)-6)/(-1*2)

x = (4*3^(1/2)-6)/(-2) or x = (-4*3^(1/2)-6)/(-2)

(x-((4*3^(1/2)-6)/(-2)))*(x-((-4*3^(1/2)-6)/(-2))) = 0

((x-((4*3^(1/2)-6)/(-2)))*(x-((-4*3^(1/2)-6)/(-2))))/(x-5) = 0

((x-((4*3^(1/2)-6)/(-2)))*(x-((-4*3^(1/2)-6)/(-2))))/(x-5) = 0 // * x-5

(x-((4*3^(1/2)-6)/(-2)))*(x-((-4*3^(1/2)-6)/(-2))) = 0

( x-((-4*3^(1/2)-6)/(-2)) )

x-((-4*3^(1/2)-6)/(-2)) = 0 // + (-4*3^(1/2)-6)/(-2)

x = (-4*3^(1/2)-6)/(-2)

( x-((4*3^(1/2)-6)/(-2)) )

x-((4*3^(1/2)-6)/(-2)) = 0 // + (4*3^(1/2)-6)/(-2)

x = (4*3^(1/2)-6)/(-2)

x in { (-4*3^(1/2)-6)/(-2), (4*3^(1/2)-6)/(-2) }

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