(-6x+18)/(x2+1)=6

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Solution for (-6x+18)/(x2+1)=6 equation:


D( x )

x^2+1 = 0

x^2+1 = 0

x^2+1 = 0

1*x^2 = -1 // : 1

x^2 = -1

x in (-oo:+oo)

(18-6*x)/(x^2+1) = 6 // - 6

(18-6*x)/(x^2+1)-6 = 0

(18-6*x)/(x^2+1)+(-6*(x^2+1))/(x^2+1) = 0

18-6*(x^2+1)-6*x = 0

12-6*x^2-6*x = 0

12-6*x^2-6*x = 0

6*(2-x^2-x) = 0

2-x^2-x = 0

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

DELTA = 9

DELTA > 0

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

x = -2 or x = 1

6*(x+2)*(x-1) = 0

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

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

6*(x+2)*(x-1) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -2, 1 }

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