(10x)/(x^2-19)=3

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Solution for (10x)/(x^2-19)=3 equation: 


D( x )

x^2-19 = 0

x^2-19 = 0

x^2-19 = 0

1*x^2 = 19 // : 1

x^2 = 19

x^2 = 19 // ^ 1/2

abs(x) = 19^(1/2)

x = 19^(1/2) or x = -19^(1/2)

x in (-oo:-19^(1/2)) U (-19^(1/2):19^(1/2)) U (19^(1/2):+oo)

(10*x)/(x^2-19) = 3 // - 3

(10*x)/(x^2-19)-3 = 0

(10*x)/(x^2-19)+(-3*(x^2-19))/(x^2-19) = 0

10*x-3*(x^2-19) = 0

10*x-3*x^2+57 = 0

10*x-3*x^2+57 = 0

10*x-3*x^2+57 = 0

DELTA = 10^2-(-3*4*57)

DELTA = 784

DELTA > 0

x = (784^(1/2)-10)/(-3*2) or x = (-784^(1/2)-10)/(-3*2)

x = -3 or x = 19/3

(x+3)*(x-19/3) = 0

((x+3)*(x-19/3))/(x^2-19) = 0

((x+3)*(x-19/3))/(x^2-19) = 0 // * x^2-19

(x+3)*(x-19/3) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-19/3 )

x-19/3 = 0 // + 19/3

x = 19/3

x in { -3, 19/3 }

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