10/(8-x)=16/3x

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Solution for 10/(8-x)=16/3x equation: 


D( x )

8-x = 0

8-x = 0

8-x = 0

8-x = 0 // - 8

-x = -8 // * -1

x = 8

x in (-oo:8) U (8:+oo)

10/(8-x) = (16/3)*x // - (16/3)*x

10/(8-x)-((16/3)*x) = 0

10/(8-x)+(-16/3)*x = 0

10/(8-x)+(-16*x)/3 = 0

(3*10)/(3*(8-x))+(-16*x*(8-x))/(3*(8-x)) = 0

3*10-16*x*(8-x) = 0

16*x^2-128*x+30 = 0

16*x^2-128*x+30 = 0

2*(8*x^2-64*x+15) = 0

8*x^2-64*x+15 = 0

DELTA = (-64)^2-(4*8*15)

DELTA = 3616

DELTA > 0

x = (3616^(1/2)+64)/(2*8) or x = (64-3616^(1/2))/(2*8)

x = (4*226^(1/2)+64)/16 or x = (64-4*226^(1/2))/16

2*(x-((64-4*226^(1/2))/16))*(x-((4*226^(1/2)+64)/16)) = 0

(2*(x-((64-4*226^(1/2))/16))*(x-((4*226^(1/2)+64)/16)))/(3*(8-x)) = 0

(2*(x-((64-4*226^(1/2))/16))*(x-((4*226^(1/2)+64)/16)))/(3*(8-x)) = 0 // * 3*(8-x)

2*(x-((64-4*226^(1/2))/16))*(x-((4*226^(1/2)+64)/16)) = 0

( 2 )

2 = 0

x belongs to the empty set

( x-((4*226^(1/2)+64)/16) )

x-((4*226^(1/2)+64)/16) = 0 // + (4*226^(1/2)+64)/16

x = (4*226^(1/2)+64)/16

( x-((64-4*226^(1/2))/16) )

x-((64-4*226^(1/2))/16) = 0 // + (64-4*226^(1/2))/16

x = (64-4*226^(1/2))/16

x in { (4*226^(1/2)+64)/16, (64-4*226^(1/2))/16 }

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