(2x)/(x-2)=5+(13x)^2/(x-2)

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Solution for (2x)/(x-2)=5+(13x)^2/(x-2) equation: 


D( x )

x-2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

(2*x)/(x-2) = ((13*x)^2)/(x-2)+5 // - ((13*x)^2)/(x-2)+5

(2*x)/(x-2)-(((13*x)^2)/(x-2))-5 = 0

(2*x)/(x-2)+(-1*169*x^2)/(x-2)-5 = 0

(2*x)/(x-2)+(-1*169*x^2)/(x-2)+(-5*(x-2))/(x-2) = 0

2*x-5*(x-2)-1*169*x^2 = 0

2*x-169*x^2-5*x+10 = 0

10-169*x^2-3*x = 0

10-169*x^2-3*x = 0

10-169*x^2-3*x = 0

DELTA = (-3)^2-(-169*4*10)

DELTA = 6769

DELTA > 0

x = (6769^(1/2)+3)/(-169*2) or x = (3-6769^(1/2))/(-169*2)

x = (6769^(1/2)+3)/(-338) or x = (3-6769^(1/2))/(-338)

(x-((6769^(1/2)+3)/(-338)))*(x-((3-6769^(1/2))/(-338))) = 0

((x-((6769^(1/2)+3)/(-338)))*(x-((3-6769^(1/2))/(-338))))/(x-2) = 0

((x-((6769^(1/2)+3)/(-338)))*(x-((3-6769^(1/2))/(-338))))/(x-2) = 0 // * x-2

(x-((6769^(1/2)+3)/(-338)))*(x-((3-6769^(1/2))/(-338))) = 0

( x-((3-6769^(1/2))/(-338)) )

x-((3-6769^(1/2))/(-338)) = 0 // + (3-6769^(1/2))/(-338)

x = (3-6769^(1/2))/(-338)

( x-((6769^(1/2)+3)/(-338)) )

x-((6769^(1/2)+3)/(-338)) = 0 // + (6769^(1/2)+3)/(-338)

x = (6769^(1/2)+3)/(-338)

x in { (3-6769^(1/2))/(-338), (6769^(1/2)+3)/(-338) }

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