(-x+2)(2x-5)/x+1=0

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Solution for (-x+2)(2x-5)/x+1=0 equation: 


D( x )

x = 0

x = 0

x = 0

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

((2-x)*(2*x-5))/x+1 = 0

((2-x)*(2*x-5))/x+(1*x)/x = 0

(2-x)*(2*x-5)+1*x = 0

10*x-2*x^2-10 = 0

10*x-2*x^2-10 = 0

2*(5*x-x^2-5) = 0

5*x-x^2-5 = 0

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

DELTA = 5

DELTA > 0

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

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

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

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

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

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

( x-((5^(1/2)+5)/2) )

x-((5^(1/2)+5)/2) = 0 // + (5^(1/2)+5)/2

x = (5^(1/2)+5)/2

( x-((5^(1/2)-5)/(-2)) )

x-((5^(1/2)-5)/(-2)) = 0 // + (5^(1/2)-5)/(-2)

x = (5^(1/2)-5)/(-2)

x in { (5^(1/2)+5)/2, (5^(1/2)-5)/(-2) }

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