4x-5/3x-4=x+10/x+6

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Solution for 4x-5/3x-4=x+10/x+6 equation: 


D( x )

x = 0

x = 0

x = 0

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

4*x-((5/3)*x)-4 = x+10/x+6 // - x+10/x+6

4*x-((5/3)*x)-x-(10/x)-6-4 = 0

4*x+(-5/3)*x-x-10*x^-1-6-4 = 0

4/3*x^1-10*x^-1-10*x^0 = 0

(4/3*x^2-10*x^1-10*x^0)/(x^1) = 0 // * x^2

x^1*(4/3*x^2-10*x^1-10*x^0) = 0

x^1

(4/3)*x^2-10*x-10 = 0

(4/3)*x^2-10*x-10 = 0

DELTA = (-10)^2-(-10*4*(4/3))

DELTA = 460/3

DELTA > 0

x = ((460/3)^(1/2)+10)/(2*(4/3)) or x = (10-(460/3)^(1/2))/(2*(4/3))

x = 3/8*((460/3)^(1/2)+10) or x = 3/8*(10-(460/3)^(1/2))

x in { 3/8*(10-(460/3)^(1/2)), 3/8*((460/3)^(1/2)+10)} 

x in { 3/8*(10-(460/3)^(1/2)), 3/8*((460/3)^(1/2)+10) }

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