(x-2)/4=8/(x-6)

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Solution for (x-2)/4=8/(x-6) equation:


D( x )

x-6 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x in (-oo:6) U (6:+oo)

(x-2)/4 = 8/(x-6) // - 8/(x-6)

(x-2)/4-(8/(x-6)) = 0

(x-2)/4-8*(x-6)^-1 = 0

(x-2)/4-8/(x-6) = 0

((x-2)*(x-6))/(4*(x-6))+(-8*4)/(4*(x-6)) = 0

(x-2)*(x-6)-8*4 = 0

x^2-8*x-20 = 0

x^2-8*x-20 = 0

x^2-8*x-20 = 0

DELTA = (-8)^2-(-20*1*4)

DELTA = 144

DELTA > 0

x = (144^(1/2)+8)/(1*2) or x = (8-144^(1/2))/(1*2)

x = 10 or x = -2

(x+2)*(x-10) = 0

((x+2)*(x-10))/(4*(x-6)) = 0

((x+2)*(x-10))/(4*(x-6)) = 0 // * 4*(x-6)

(x+2)*(x-10) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-10 )

x-10 = 0 // + 10

x = 10

x in { -2, 10 }

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