5-6x/7+3x=2(1-x)/x

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Solution for 5-6x/7+3x=2(1-x)/x equation:


D( x )

x = 0

x = 0

x = 0

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

3*x-((6*x)/7)+5 = (2*(1-x))/x // - (2*(1-x))/x

3*x-((2*(1-x))/x)-((6*x)/7)+5 = 0

(-6/7)*x-2*x^-1*(1-x)+3*x+5 = 0

(-6*x)/7-2*x^-1*(1-x)+3*x+5 = 0

(-2*7*x^-1*(1-x))/7+(-6*x)/7+(3*7*x)/7+(5*7)/7 = 0

3*7*x-2*7*x^-1*(1-x)-6*x+5*7 = 0

21*x-6*x-14*x^-1+14+35 = 0

15*x-14*x^-1+14+35 = 0

15*x-14*x^-1+49 = 0

15*x-14*x^-1+49 = 0

15*x^1-14*x^-1+49*x^0 = 0

(15*x^2+49*x^1-14*x^0)/(x^1) = 0 // * x^2

x^1*(15*x^2+49*x^1-14*x^0) = 0

x^1

15*x^2+49*x-14 = 0

15*x^2+49*x-14 = 0

DELTA = 49^2-(-14*4*15)

DELTA = 3241

DELTA > 0

x = (3241^(1/2)-49)/(2*15) or x = (-3241^(1/2)-49)/(2*15)

x = (3241^(1/2)-49)/30 or x = (-(3241^(1/2)+49))/30

x in { (-(3241^(1/2)+49))/30, (3241^(1/2)-49)/30}

(x+(3241^(1/2)+49)/30)*(x-((3241^(1/2)-49)/30)) = 0

((x+(3241^(1/2)+49)/30)*(x-((3241^(1/2)-49)/30)))/7 = 0

((x+(3241^(1/2)+49)/30)*(x-((3241^(1/2)-49)/30)))/7 = 0 // * 7

(x+(3241^(1/2)+49)/30)*(x-((3241^(1/2)-49)/30)) = 0

( x+(3241^(1/2)+49)/30 )

x+(3241^(1/2)+49)/30 = 0 // - (3241^(1/2)+49)/30

x = -((3241^(1/2)+49)/30)

( x-((3241^(1/2)-49)/30) )

x-((3241^(1/2)-49)/30) = 0 // + (3241^(1/2)-49)/30

x = (3241^(1/2)-49)/30

x in { -((3241^(1/2)+49)/30), (3241^(1/2)-49)/30 }

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