(20+x)/5y=2y/x

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Solution for (20+x)/5y=2y/x equation:


D( x )

x = 0

x = 0

x = 0

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

y*((x+20)/5) = (2*y)/x // - (2*y)/x

y*((x+20)/5)-((2*y)/x) = 0

y*((x+20)/5)-2*x^-1*y = 0

(y*(x+20))/5+(-2*y)/x = 0

(x*y*(x+20))/(5*x)+(-2*5*y)/(5*x) = 0

x*y*(x+20)-2*5*y = 0

x^2*y+20*x*y-10*y = 0

x^2*y+20*x*y-10*y = 0

y*(x^2+20*x-10) = 0

x^2+20*x-10 = 0

DELTA = 20^2-(-10*1*4)

DELTA = 440

DELTA > 0

x = (440^(1/2)-20)/(1*2) or x = (-440^(1/2)-20)/(1*2)

x = (2*110^(1/2)-20)/2 or x = (-2*110^(1/2)-20)/2

y*(x-((-2*110^(1/2)-20)/2))*(x-((2*110^(1/2)-20)/2)) = 0

(y*(x-((-2*110^(1/2)-20)/2))*(x-((2*110^(1/2)-20)/2)))/(5*x) = 0

(y*(x-((-2*110^(1/2)-20)/2))*(x-((2*110^(1/2)-20)/2)))/(5*x) = 0 // * 5*x

y*(x-((-2*110^(1/2)-20)/2))*(x-((2*110^(1/2)-20)/2)) = 0

( x-((-2*110^(1/2)-20)/2) )

x-((-2*110^(1/2)-20)/2) = 0 // + (-2*110^(1/2)-20)/2

x = (-2*110^(1/2)-20)/2

( x-((2*110^(1/2)-20)/2) )

x-((2*110^(1/2)-20)/2) = 0 // + (2*110^(1/2)-20)/2

x = (2*110^(1/2)-20)/2

x in { (-2*110^(1/2)-20)/2, (2*110^(1/2)-20)/2 }

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