3/4=4/(x-1)-x

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Solution for 3/4=4/(x-1)-x equation: 


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

3/4 = 4/(x-1)-x // - 4/(x-1)-x

x-(4/(x-1))+3/4 = 0

x-4*(x-1)^-1+3/4 = 0

x-4/(x-1)+3/4 = 0

(-4*4)/(4*(x-1))+(4*x*(x-1))/(4*(x-1))+(3*(x-1))/(4*(x-1)) = 0

4*x*(x-1)+3*(x-1)-4*4 = 0

4*x^2-4*x+3*x-16-3 = 0

4*x^2-x-19 = 0

4*x^2-x-19 = 0

4*x^2-x-19 = 0

DELTA = (-1)^2-(-19*4*4)

DELTA = 305

DELTA > 0

x = (305^(1/2)+1)/(2*4) or x = (1-305^(1/2))/(2*4)

x = (305^(1/2)+1)/8 or x = (1-305^(1/2))/8

(x-((1-305^(1/2))/8))*(x-((305^(1/2)+1)/8)) = 0

((x-((1-305^(1/2))/8))*(x-((305^(1/2)+1)/8)))/(4*(x-1)) = 0

((x-((1-305^(1/2))/8))*(x-((305^(1/2)+1)/8)))/(4*(x-1)) = 0 // * 4*(x-1)

(x-((1-305^(1/2))/8))*(x-((305^(1/2)+1)/8)) = 0

( x-((1-305^(1/2))/8) )

x-((1-305^(1/2))/8) = 0 // + (1-305^(1/2))/8

x = (1-305^(1/2))/8

( x-((305^(1/2)+1)/8) )

x-((305^(1/2)+1)/8) = 0 // + (305^(1/2)+1)/8

x = (305^(1/2)+1)/8

x in { (1-305^(1/2))/8, (305^(1/2)+1)/8 }

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