(3/4x+1)+(7/x+9)=13/10x

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Solution for (3/4x+1)+(7/x+9)=13/10x equation:


D( x )

x = 0

x = 0

x = 0

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

(3/4)*x+7/x+1+9 = (13/10)*x // - (13/10)*x

(3/4)*x-((13/10)*x)+7/x+1+9 = 0

(3/4)*x+(-13/10)*x+7/x+1+9 = 0

7*x^-1-11/20*x^1+10*x^0 = 0

(10*x^1-11/20*x^2+7*x^0)/(x^1) = 0 // * x^2

x^1*(10*x^1-11/20*x^2+7*x^0) = 0

x^1

(-11/20)*x^2+10*x+7 = 0

(-11/20)*x^2+10*x+7 = 0

DELTA = 10^2-(4*7*(-11/20))

DELTA = 577/5

DELTA > 0

x = ((577/5)^(1/2)-10)/(2*(-11/20)) or x = (-(577/5)^(1/2)-10)/(2*(-11/20))

x = -10/11*((577/5)^(1/2)-10) or x = 10/11*((577/5)^(1/2)+10)

x in { -10/11*((577/5)^(1/2)-10), 10/11*((577/5)^(1/2)+10)}

x in { -10/11*((577/5)^(1/2)-10), 10/11*((577/5)^(1/2)+10) }

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