3=40x/(x^2-9)

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Solution for 3=40x/(x^2-9) equation: 


D( x )

x^2-9 = 0

x^2-9 = 0

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x in (-oo:-3) U (-3:3) U (3:+oo)

3 = (40*x)/(x^2-9) // - (40*x)/(x^2-9)

3-((40*x)/(x^2-9)) = 0

3-40*x*(x^2-9)^-1 = 0

(-40*x)/(x^2-9)+3 = 0

(-40*x)/(x^2-9)+(3*(x^2-9))/(x^2-9) = 0

3*(x^2-9)-40*x = 0

3*x^2-40*x-27 = 0

3*x^2-40*x-27 = 0

3*x^2-40*x-27 = 0

DELTA = (-40)^2-(-27*3*4)

DELTA = 1924

DELTA > 0

x = (1924^(1/2)+40)/(2*3) or x = (40-1924^(1/2))/(2*3)

x = (2*481^(1/2)+40)/6 or x = (40-2*481^(1/2))/6

(x-((40-2*481^(1/2))/6))*(x-((2*481^(1/2)+40)/6)) = 0

((x-((40-2*481^(1/2))/6))*(x-((2*481^(1/2)+40)/6)))/(x^2-9) = 0

((x-((40-2*481^(1/2))/6))*(x-((2*481^(1/2)+40)/6)))/(x^2-9) = 0 // * x^2-9

(x-((40-2*481^(1/2))/6))*(x-((2*481^(1/2)+40)/6)) = 0

( x-((2*481^(1/2)+40)/6) )

x-((2*481^(1/2)+40)/6) = 0 // + (2*481^(1/2)+40)/6

x = (2*481^(1/2)+40)/6

( x-((40-2*481^(1/2))/6) )

x-((40-2*481^(1/2))/6) = 0 // + (40-2*481^(1/2))/6

x = (40-2*481^(1/2))/6

x in { (2*481^(1/2)+40)/6, (40-2*481^(1/2))/6 }

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