(10/3x)-((x+1)/x)=5/8

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Solution for (10/3x)-((x+1)/x)=5/8 equation:


D( x )

x = 0

x = 0

x = 0

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

(10/3)*x-((x+1)/x) = 5/8 // - 5/8

(10/3)*x-((x+1)/x)-(5/8) = 0

(10/3)*x-((x+1)/x)-5/8 = 0

(-1*(x+1))/x+(10*x)/3-5/8 = 0

(-1*3*8*(x+1))/(3*8*x)+(8*10*x*x)/(3*8*x)+(-5*3*x)/(3*8*x) = 0

8*10*x*x-1*3*8*(x+1)-5*3*x = 0

80*x^2-24*x-15*x-24 = 0

80*x^2-39*x-24 = 0

80*x^2-39*x-24 = 0

80*x^2-39*x-24 = 0

DELTA = (-39)^2-(-24*4*80)

DELTA = 9201

DELTA > 0

x = (9201^(1/2)+39)/(2*80) or x = (39-9201^(1/2))/(2*80)

x = (9201^(1/2)+39)/160 or x = (39-9201^(1/2))/160

(x-((39-9201^(1/2))/160))*(x-((9201^(1/2)+39)/160)) = 0

((x-((39-9201^(1/2))/160))*(x-((9201^(1/2)+39)/160)))/(3*8*x) = 0

((x-((39-9201^(1/2))/160))*(x-((9201^(1/2)+39)/160)))/(3*8*x) = 0 // * 3*8*x

(x-((39-9201^(1/2))/160))*(x-((9201^(1/2)+39)/160)) = 0

( x-((39-9201^(1/2))/160) )

x-((39-9201^(1/2))/160) = 0 // + (39-9201^(1/2))/160

x = (39-9201^(1/2))/160

( x-((9201^(1/2)+39)/160) )

x-((9201^(1/2)+39)/160) = 0 // + (9201^(1/2)+39)/160

x = (9201^(1/2)+39)/160

x in { (39-9201^(1/2))/160, (9201^(1/2)+39)/160 }

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