(3/2)-((x-5)/x)=x/5

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Solution for (3/2)-((x-5)/x)=x/5 equation:


D( x )

x = 0

x = 0

x = 0

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

3/2-((x-5)/x) = x/5 // - x/5

3/2-((x-5)/x)-(x/5) = 0

(-1*(x-5))/x-x/5+3/2 = 0

(-1*2*5*(x-5))/(2*5*x)+(2*(-x)*x)/(2*5*x)+(3*5*x)/(2*5*x) = 0

2*(-x)*x-1*2*5*(x-5)+3*5*x = 0

15*x-2*x^2-10*x+50 = 0

5*x-2*x^2+50 = 0

5*x-2*x^2+50 = 0

5*x-2*x^2+50 = 0

DELTA = 5^2-(-2*4*50)

DELTA = 425

DELTA > 0

x = (425^(1/2)-5)/(-2*2) or x = (-425^(1/2)-5)/(-2*2)

x = (5*17^(1/2)-5)/(-4) or x = (-5*17^(1/2)-5)/(-4)

(x-((5*17^(1/2)-5)/(-4)))*(x-((-5*17^(1/2)-5)/(-4))) = 0

((x-((5*17^(1/2)-5)/(-4)))*(x-((-5*17^(1/2)-5)/(-4))))/(2*5*x) = 0

((x-((5*17^(1/2)-5)/(-4)))*(x-((-5*17^(1/2)-5)/(-4))))/(2*5*x) = 0 // * 2*5*x

(x-((5*17^(1/2)-5)/(-4)))*(x-((-5*17^(1/2)-5)/(-4))) = 0

( x-((-5*17^(1/2)-5)/(-4)) )

x-((-5*17^(1/2)-5)/(-4)) = 0 // + (-5*17^(1/2)-5)/(-4)

x = (-5*17^(1/2)-5)/(-4)

( x-((5*17^(1/2)-5)/(-4)) )

x-((5*17^(1/2)-5)/(-4)) = 0 // + (5*17^(1/2)-5)/(-4)

x = (5*17^(1/2)-5)/(-4)

x in { (-5*17^(1/2)-5)/(-4), (5*17^(1/2)-5)/(-4) }

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