500/(200+x)+1/2=500/(200-x)

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Solution for 500/(200+x)+1/2=500/(200-x) equation: 


D( x )

200-x = 0

x+200 = 0

200-x = 0

200-x = 0

200-x = 0 // - 200

-x = -200 // * -1

x = 200

x+200 = 0

x+200 = 0

x+200 = 0 // - 200

x = -200

x in (-oo:-200) U (-200:200) U (200:+oo)

500/(x+200)+1/2 = 500/(200-x) // - 500/(200-x)

500/(x+200)-(500/(200-x))+1/2 = 0

500/(x+200)-500*(200-x)^-1+1/2 = 0

500/(x+200)-500/(200-x)+1/2 = 0

(2*500*(200-x))/(2*(x+200)*(200-x))+(-500*2*(x+200))/(2*(x+200)*(200-x))+(1*(x+200)*(200-x))/(2*(x+200)*(200-x)) = 0

2*500*(200-x)-500*2*(x+200)+1*(x+200)*(200-x) = 0

40000-x^2-2000*x = 0

40000-x^2-2000*x = 0

40000-x^2-2000*x = 0

DELTA = (-2000)^2-(-1*4*40000)

DELTA = 4160000

DELTA > 0

x = (4160000^(1/2)+2000)/(-1*2) or x = (2000-4160000^(1/2))/(-1*2)

x = (400*26^(1/2)+2000)/(-2) or x = (2000-400*26^(1/2))/(-2)

(x-((400*26^(1/2)+2000)/(-2)))*(x-((2000-400*26^(1/2))/(-2))) = 0

((x-((400*26^(1/2)+2000)/(-2)))*(x-((2000-400*26^(1/2))/(-2))))/(2*(x+200)*(200-x)) = 0

((x-((400*26^(1/2)+2000)/(-2)))*(x-((2000-400*26^(1/2))/(-2))))/(2*(x+200)*(200-x)) = 0 // * 2*(x+200)*(200-x)

(x-((400*26^(1/2)+2000)/(-2)))*(x-((2000-400*26^(1/2))/(-2))) = 0

( x-((2000-400*26^(1/2))/(-2)) )

x-((2000-400*26^(1/2))/(-2)) = 0 // + (2000-400*26^(1/2))/(-2)

x = (2000-400*26^(1/2))/(-2)

( x-((400*26^(1/2)+2000)/(-2)) )

x-((400*26^(1/2)+2000)/(-2)) = 0 // + (400*26^(1/2)+2000)/(-2)

x = (400*26^(1/2)+2000)/(-2)

x in { (2000-400*26^(1/2))/(-2), (400*26^(1/2)+2000)/(-2) }

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