((5x-3))/(x^2+2x-8)=3/7

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Solution for ((5x-3))/(x^2+2x-8)=3/7 equation: 


D( x )

x^2+2*x-8 = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

DELTA = 2^2-(-8*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)-2)/(1*2) or x = (-36^(1/2)-2)/(1*2)

x = 2 or x = -4

x in (-oo:-4) U (-4:2) U (2:+oo)

(5*x-3)/(x^2+2*x-8) = 3/7 // - 3/7

(5*x-3)/(x^2+2*x-8)-(3/7) = 0

(5*x-3)/(x^2+2*x-8)-3/7 = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

DELTA = 2^2-(-8*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)-2)/(1*2) or x = (-36^(1/2)-2)/(1*2)

x = 2 or x = -4

(x+4)*(x-2) = 0

(5*x-3)/((x+4)*(x-2))-3/7 = 0

(7*(5*x-3))/(7*(x+4)*(x-2))+(-3*(x+4)*(x-2))/(7*(x+4)*(x-2)) = 0

7*(5*x-3)-3*(x+4)*(x-2) = 0

29*x-3*x^2+3 = 0

29*x-3*x^2+3 = 0

29*x-3*x^2+3 = 0

DELTA = 29^2-(-3*3*4)

DELTA = 877

DELTA > 0

x = (877^(1/2)-29)/(-3*2) or x = (-877^(1/2)-29)/(-3*2)

x = (877^(1/2)-29)/(-6) or x = (877^(1/2)+29)/6

(x-((877^(1/2)-29)/(-6)))*(x-((877^(1/2)+29)/6)) = 0

((x-((877^(1/2)-29)/(-6)))*(x-((877^(1/2)+29)/6)))/(7*(x+4)*(x-2)) = 0

((x-((877^(1/2)-29)/(-6)))*(x-((877^(1/2)+29)/6)))/(7*(x+4)*(x-2)) = 0 // * 7*(x+4)*(x-2)

(x-((877^(1/2)-29)/(-6)))*(x-((877^(1/2)+29)/6)) = 0

( x-((877^(1/2)+29)/6) )

x-((877^(1/2)+29)/6) = 0 // + (877^(1/2)+29)/6

x = (877^(1/2)+29)/6

( x-((877^(1/2)-29)/(-6)) )

x-((877^(1/2)-29)/(-6)) = 0 // + (877^(1/2)-29)/(-6)

x = (877^(1/2)-29)/(-6)

x in { (877^(1/2)+29)/6, (877^(1/2)-29)/(-6) }

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