(1/2x+3)=(7/x+4)

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Solution for (1/2x+3)=(7/x+4) equation: 


D( x )

x = 0

x = 0

x = 0

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

(1/2)*x+3 = 7/x+4 // - 7/x+4

(1/2)*x-(7/x)-4+3 = 0

(1/2)*x-7*x^-1-4+3 = 0

1/2*x^1-7*x^-1-1*x^0 = 0

(1/2*x^2-1*x^1-7*x^0)/(x^1) = 0 // * x^2

x^1*(1/2*x^2-1*x^1-7*x^0) = 0

x^1

(1/2)*x^2-x-7 = 0

(1/2)*x^2-x-7 = 0

DELTA = (-1)^2-(-7*4*(1/2))

DELTA = 15

DELTA > 0

x = (15^(1/2)+1)/(2*(1/2)) or x = (1-15^(1/2))/(2*(1/2))

x = 15^(1/2)+1 or x = 1-15^(1/2)

x in { 1-15^(1/2), 15^(1/2)+1} 

x in { 1-15^(1/2), 15^(1/2)+1 }

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