1/4+1/(x+2)=x

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Solution for 1/4+1/(x+2)=x equation: 


D( x )

x+2 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x in (-oo:-2) U (-2:+oo)

1/(x+2)+1/4 = x // - x

1/(x+2)-x+1/4 = 0

(1*4)/(4*(x+2))+(4*(-x)*(x+2))/(4*(x+2))+(1*(x+2))/(4*(x+2)) = 0

4*(-x)*(x+2)+1*(x+2)+1*4 = 0

x-4*x^2-8*x+2+4 = 0

6-4*x^2-7*x = 0

6-4*x^2-7*x = 0

6-4*x^2-7*x = 0

DELTA = (-7)^2-(-4*4*6)

DELTA = 145

DELTA > 0

x = (145^(1/2)+7)/(-4*2) or x = (7-145^(1/2))/(-4*2)

x = (145^(1/2)+7)/(-8) or x = (7-145^(1/2))/(-8)

(x-((145^(1/2)+7)/(-8)))*(x-((7-145^(1/2))/(-8))) = 0

((x-((145^(1/2)+7)/(-8)))*(x-((7-145^(1/2))/(-8))))/(4*(x+2)) = 0

((x-((145^(1/2)+7)/(-8)))*(x-((7-145^(1/2))/(-8))))/(4*(x+2)) = 0 // * 4*(x+2)

(x-((145^(1/2)+7)/(-8)))*(x-((7-145^(1/2))/(-8))) = 0

( x-((145^(1/2)+7)/(-8)) )

x-((145^(1/2)+7)/(-8)) = 0 // + (145^(1/2)+7)/(-8)

x = (145^(1/2)+7)/(-8)

( x-((7-145^(1/2))/(-8)) )

x-((7-145^(1/2))/(-8)) = 0 // + (7-145^(1/2))/(-8)

x = (7-145^(1/2))/(-8)

x in { (145^(1/2)+7)/(-8), (7-145^(1/2))/(-8) }

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