-10/(x-9)=x/2

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Solution for -10/(x-9)=x/2 equation:


D( x )

x-9 = 0

x-9 = 0

x-9 = 0

x-9 = 0 // + 9

x = 9

x in (-oo:9) U (9:+oo)

-10/(x-9) = x/2 // - x/2

-10/(x-9)-(x/2) = 0

-10/(x-9)-x/2 = 0

(-10*2)/(2*(x-9))+(-x*(x-9))/(2*(x-9)) = 0

-x*(x-9)-10*2 = 0

9*x-x^2-20 = 0

9*x-x^2-20 = 0

9*x-x^2-20 = 0

DELTA = 9^2-(-20*(-1)*4)

DELTA = 1

DELTA > 0

x = (1^(1/2)-9)/(-1*2) or x = (-1^(1/2)-9)/(-1*2)

x = 4 or x = 5

(x-4)*(x-5) = 0

((x-4)*(x-5))/(2*(x-9)) = 0

((x-4)*(x-5))/(2*(x-9)) = 0 // * 2*(x-9)

(x-4)*(x-5) = 0

( x-4 )

x-4 = 0 // + 4

x = 4

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 4, 5 }

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