2/3x-5/x=7/10-3/2x+1

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Solution for 2/3x-5/x=7/10-3/2x+1 equation:


D( x )

x = 0

x = 0

x = 0

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

(2/3)*x-(5/x) = 7/10-((3/2)*x)+1 // - 7/10-((3/2)*x)+1

(2/3)*x+(3/2)*x-(5/x)-(7/10)-1 = 0

(2/3)*x+(3/2)*x-5*x^-1-7/10-1 = 0

13/6*x^1-5*x^-1-17/10*x^0 = 0

(13/6*x^2-17/10*x^1-5*x^0)/(x^1) = 0 // * x^2

x^1*(13/6*x^2-17/10*x^1-5*x^0) = 0

x^1

(13/6)*x^2+(-17/10)*x-5 = 0

(13/6)*x^2+(-17/10)*x-5 = 0

DELTA = (-17/10)^2-(-5*4*(13/6))

DELTA = 13867/300

DELTA > 0

x = ((13867/300)^(1/2)-(-17/10))/(2*(13/6)) or x = (-(-17/10)-(13867/300)^(1/2))/(2*(13/6))

x = 3/13*((13867/300)^(1/2)+17/10) or x = 3/13*(17/10-(13867/300)^(1/2))

x in { 3/13*(17/10-(13867/300)^(1/2)), 3/13*((13867/300)^(1/2)+17/10)}

x in { 3/13*(17/10-(13867/300)^(1/2)), 3/13*((13867/300)^(1/2)+17/10) }

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