((x+5)/(14))=(4/7)/((x-4)/8)

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Solution for ((x+5)/(14))=(4/7)/((x-4)/8) equation: 


D( x )

(x-4)/8 = 0

(x-4)/8 = 0

(x-4)/8 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:4) U (4:+oo)

(x+5)/14 = (4/7)/((x-4)/8) // - (4/7)/((x-4)/8)

(x+5)/14-((4/7)/((x-4)/8)) = 0

(x+5)/14+(-32/7)*(x-4)^-1 = 0

(x+5)/14-32/7/(x-4) = 0

((x+5)*(x-4))/(14*(x-4))+(-32/7*14)/(14*(x-4)) = 0

(x+5)*(x-4)-32/7*14 = 0

x^2+x-84 = 0

x^2+x-84 = 0

x^2+x-84 = 0

DELTA = 1^2-(-84*1*4)

DELTA = 337

DELTA > 0

x = (337^(1/2)-1)/(1*2) or x = (-337^(1/2)-1)/(1*2)

x = (337^(1/2)-1)/2 or x = (-(337^(1/2)+1))/2

(x+(337^(1/2)+1)/2)*(x-((337^(1/2)-1)/2)) = 0

((x+(337^(1/2)+1)/2)*(x-((337^(1/2)-1)/2)))/(14*(x-4)) = 0

((x+(337^(1/2)+1)/2)*(x-((337^(1/2)-1)/2)))/(14*(x-4)) = 0 // * 14*(x-4)

(x+(337^(1/2)+1)/2)*(x-((337^(1/2)-1)/2)) = 0

( x+(337^(1/2)+1)/2 )

x+(337^(1/2)+1)/2 = 0 // - (337^(1/2)+1)/2

x = -((337^(1/2)+1)/2)

( x-((337^(1/2)-1)/2) )

x-((337^(1/2)-1)/2) = 0 // + (337^(1/2)-1)/2

x = (337^(1/2)-1)/2

x in { -((337^(1/2)+1)/2), (337^(1/2)-1)/2 }

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