3x/(x-6)(x+6)/4x/x+6

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Solution for 3x/(x-6)(x+6)/4x/x+6 equation: 


D( x )

x-6 = 0

x = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x = 0

x = 0

x in (-oo:0) U (0:6) U (6:+oo)

(x*((((3*x)/(x-6))*(x+6))/4))/x+6 = 0

(3*x*(x+6))/(4*(x-6))+6 = 0

(3*x*(x+6))/(4*(x-6))+(4*6*(x-6))/(4*(x-6)) = 0

3*x*(x+6)+4*6*(x-6) = 0

3*x^2+42*x-144 = 0

3*x^2+42*x-144 = 0

3*(x^2+14*x-48) = 0

x^2+14*x-48 = 0

DELTA = 14^2-(-48*1*4)

DELTA = 388

DELTA > 0

x = (388^(1/2)-14)/(1*2) or x = (-388^(1/2)-14)/(1*2)

x = (2*97^(1/2)-14)/2 or x = (-2*97^(1/2)-14)/2

3*(x-((-2*97^(1/2)-14)/2))*(x-((2*97^(1/2)-14)/2)) = 0

(3*(x-((-2*97^(1/2)-14)/2))*(x-((2*97^(1/2)-14)/2)))/(4*(x-6)) = 0

(3*(x-((-2*97^(1/2)-14)/2))*(x-((2*97^(1/2)-14)/2)))/(4*(x-6)) = 0 // * 4*(x-6)

3*(x-((-2*97^(1/2)-14)/2))*(x-((2*97^(1/2)-14)/2)) = 0

( x-((-2*97^(1/2)-14)/2) )

x-((-2*97^(1/2)-14)/2) = 0 // + (-2*97^(1/2)-14)/2

x = (-2*97^(1/2)-14)/2

( x-((2*97^(1/2)-14)/2) )

x-((2*97^(1/2)-14)/2) = 0 // + (2*97^(1/2)-14)/2

x = (2*97^(1/2)-14)/2

x in { (-2*97^(1/2)-14)/2, (2*97^(1/2)-14)/2 }

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