(1/3(x+5))-(2/3x)=1/x+5

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Solution for (1/3(x+5))-(2/3x)=1/x+5 equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

5*x-x^2-15*x-3 = 0

-x^2-10*x-3 = 0

-x^2-10*x-3 = 0

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

x^2+10*x+3 = 0

DELTA = 10^2-(1*3*4)

DELTA = 88

DELTA > 0

x = (88^(1/2)-10)/(1*2) or x = (-88^(1/2)-10)/(1*2)

x = (2*22^(1/2)-10)/2 or x = (-2*22^(1/2)-10)/2

-1*(x-((-2*22^(1/2)-10)/2))*(x-((2*22^(1/2)-10)/2)) = 0

(-1*(x-((-2*22^(1/2)-10)/2))*(x-((2*22^(1/2)-10)/2)))/(3*x) = 0

(-1*(x-((-2*22^(1/2)-10)/2))*(x-((2*22^(1/2)-10)/2)))/(3*x) = 0 // * 3*x

-1*(x-((-2*22^(1/2)-10)/2))*(x-((2*22^(1/2)-10)/2)) = 0

( x-((-2*22^(1/2)-10)/2) )

x-((-2*22^(1/2)-10)/2) = 0 // + (-2*22^(1/2)-10)/2

x = (-2*22^(1/2)-10)/2

( x-((2*22^(1/2)-10)/2) )

x-((2*22^(1/2)-10)/2) = 0 // + (2*22^(1/2)-10)/2

x = (2*22^(1/2)-10)/2

x in { (-2*22^(1/2)-10)/2, (2*22^(1/2)-10)/2 }

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