(228*3.5)/((1-x)*228)+(x*3.5)=14

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Solution for (228*3.5)/((1-x)*228)+(x*3.5)=14 equation: 


D( x )

228*(1-x) = 0

228*(1-x) = 0

228*(1-x) = 0

1-x = 0 // - 1

-x = -1 // * -1

x = 1

x in (-oo:1) U (1:+oo)

(3.5*228)/(228*(1-x))+3.5*x = 14 // - 14

(3.5*228)/(228*(1-x))+3.5*x-14 = 0

798/(228*(1-x))+3.5*x-14 = 0

798/(228*(1-x))+(3.5*228*x*(1-x))/(228*(1-x))+(-14*228*(1-x))/(228*(1-x)) = 0

3.5*228*x*(1-x)-14*228*(1-x)+798 = 0

798*x-798*x^2+3192*x-3192+798 = 0

3990*x-798*x^2-2394 = 0

3990*x-798*x^2-2394 = 0

798*(5*x-x^2-3) = 0

5*x-x^2-3 = 0

DELTA = 5^2-(-3*(-1)*4)

DELTA = 13

DELTA > 0

x = (13^(1/2)-5)/(-1*2) or x = (-13^(1/2)-5)/(-1*2)

x = (13^(1/2)-5)/(-2) or x = (13^(1/2)+5)/2

798*(x-((13^(1/2)-5)/(-2)))*(x-((13^(1/2)+5)/2)) = 0

(798*(x-((13^(1/2)-5)/(-2)))*(x-((13^(1/2)+5)/2)))/(228*(1-x)) = 0

(798*(x-((13^(1/2)-5)/(-2)))*(x-((13^(1/2)+5)/2)))/(228*(1-x)) = 0 // * 228*(1-x)

798*(x-((13^(1/2)-5)/(-2)))*(x-((13^(1/2)+5)/2)) = 0

( x-((13^(1/2)+5)/2) )

x-((13^(1/2)+5)/2) = 0 // + (13^(1/2)+5)/2

x = (13^(1/2)+5)/2

( x-((13^(1/2)-5)/(-2)) )

x-((13^(1/2)-5)/(-2)) = 0 // + (13^(1/2)-5)/(-2)

x = (13^(1/2)-5)/(-2)

x in { (13^(1/2)+5)/2, (13^(1/2)-5)/(-2) }

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