(10x-30)/(x-3)=x

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Solution for (10x-30)/(x-3)=x equation: 


D( x )

x-3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

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

(10*x-30)/(x-3) = x // - x

(10*x-30)/(x-3)-x = 0

(10*x-30)/(x-3)+(-x*(x-3))/(x-3) = 0

10*x-x*(x-3)-30 = 0

13*x-x^2-30 = 0

13*x-x^2-30 = 0

13*x-x^2-30 = 0

DELTA = 13^2-(-30*(-1)*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-13)/(-1*2) or x = (-49^(1/2)-13)/(-1*2)

x = 3 or x = 10

(x-3)*(x-10) = 0

((x-3)*(x-10))/(x-3) = 0

((x-3)*(x-10))/(x-3) = 0 // * x-3

(x-3)*(x-10) = 0

( x-10 )

x-10 = 0 // + 10

x = 10

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x = 10

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