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

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Solution for (x-1)^-1/2(x-7)+4(x-1)^1/2=0 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)

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

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

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

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

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

4*x^2-7*x-3 = 0

4*x^2-7*x-3 = 0

4*x^2-7*x-3 = 0

DELTA = (-7)^2-(-3*4*4)

DELTA = 97

DELTA > 0

x = (97^(1/2)+7)/(2*4) or x = (7-97^(1/2))/(2*4)

x = (97^(1/2)+7)/8 or x = (7-97^(1/2))/8

(x-((7-97^(1/2))/8))*(x-((97^(1/2)+7)/8)) = 0

((x-((7-97^(1/2))/8))*(x-((97^(1/2)+7)/8)))/(2*(x-1)) = 0

((x-((7-97^(1/2))/8))*(x-((97^(1/2)+7)/8)))/(2*(x-1)) = 0 // * 2*(x-1)

(x-((7-97^(1/2))/8))*(x-((97^(1/2)+7)/8)) = 0

( x-((7-97^(1/2))/8) )

x-((7-97^(1/2))/8) = 0 // + (7-97^(1/2))/8

x = (7-97^(1/2))/8

( x-((97^(1/2)+7)/8) )

x-((97^(1/2)+7)/8) = 0 // + (97^(1/2)+7)/8

x = (97^(1/2)+7)/8

x in { (7-97^(1/2))/8, (97^(1/2)+7)/8 }

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