(7x)/(29x+30)=(1)/(x)

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Solution for (7x)/(29x+30)=(1)/(x) equation:


D( x )

x = 0

29*x+30 = 0

x = 0

x = 0

29*x+30 = 0

29*x+30 = 0

29*x+30 = 0 // - 30

29*x = -30 // : 29

x = -30/29

x in (-oo:-30/29) U (-30/29:0) U (0:+oo)

(7*x)/(29*x+30) = 1/x // - 1/x

(7*x)/(29*x+30)-(1/x) = 0

(7*x)/(29*x+30)-x^-1 = 0

(7*x)/(29*x+30)-1/x = 0

(7*x*x)/(x*(29*x+30))+(-1*(29*x+30))/(x*(29*x+30)) = 0

7*x*x-1*(29*x+30) = 0

7*x^2-29*x-30 = 0

7*x^2-29*x-30 = 0

7*x^2-29*x-30 = 0

DELTA = (-29)^2-(-30*4*7)

DELTA = 1681

DELTA > 0

x = (1681^(1/2)+29)/(2*7) or x = (29-1681^(1/2))/(2*7)

x = 5 or x = -6/7

(x+6/7)*(x-5) = 0

((x+6/7)*(x-5))/(x*(29*x+30)) = 0

((x+6/7)*(x-5))/(x*(29*x+30)) = 0 // * x*(29*x+30)

(x+6/7)*(x-5) = 0

( x+6/7 )

x+6/7 = 0 // - 6/7

x = -6/7

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -6/7, 5 }

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