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

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


D( x )

x+4 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

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

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

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

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

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

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

7*x*(x+4)-10*x*(x+4)+1*7 = 0

7*x^2-10*x^2+28*x-40*x+7 = 0

7-3*x^2-12*x = 0

7-3*x^2-12*x = 0

7-3*x^2-12*x = 0

DELTA = (-12)^2-(-3*4*7)

DELTA = 228

DELTA > 0

x = (228^(1/2)+12)/(-3*2) or x = (12-228^(1/2))/(-3*2)

x = (2*57^(1/2)+12)/(-6) or x = (12-2*57^(1/2))/(-6)

(x-((2*57^(1/2)+12)/(-6)))*(x-((12-2*57^(1/2))/(-6))) = 0

((x-((2*57^(1/2)+12)/(-6)))*(x-((12-2*57^(1/2))/(-6))))/(7*(x+4)) = 0

((x-((2*57^(1/2)+12)/(-6)))*(x-((12-2*57^(1/2))/(-6))))/(7*(x+4)) = 0 // * 7*(x+4)

(x-((2*57^(1/2)+12)/(-6)))*(x-((12-2*57^(1/2))/(-6))) = 0

( x-((12-2*57^(1/2))/(-6)) )

x-((12-2*57^(1/2))/(-6)) = 0 // + (12-2*57^(1/2))/(-6)

x = (12-2*57^(1/2))/(-6)

( x-((2*57^(1/2)+12)/(-6)) )

x-((2*57^(1/2)+12)/(-6)) = 0 // + (2*57^(1/2)+12)/(-6)

x = (2*57^(1/2)+12)/(-6)

x in { (12-2*57^(1/2))/(-6), (2*57^(1/2)+12)/(-6) }

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