3(x-1)/9x=243

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Solution for 3(x-1)/9x=243 equation:


x in (-oo:+oo)

x*((3*(x-1))/9) = 243 // - 243

x*((3*(x-1))/9)-243 = 0

(3*x*(x-1))/9-243 = 0

(3*x*(x-1))/9+(-243*9)/9 = 0

3*x*(x-1)-243*9 = 0

3*x^2-3*x-2187 = 0

3*x^2-3*x-2187 = 0

3*(x^2-x-729) = 0

x^2-x-729 = 0

DELTA = (-1)^2-(-729*1*4)

DELTA = 2917

DELTA > 0

x = (2917^(1/2)+1)/(1*2) or x = (1-2917^(1/2))/(1*2)

x = (2917^(1/2)+1)/2 or x = (1-2917^(1/2))/2

3*(x-((1-2917^(1/2))/2))*(x-((2917^(1/2)+1)/2)) = 0

(3*(x-((1-2917^(1/2))/2))*(x-((2917^(1/2)+1)/2)))/9 = 0

(3*(x-((1-2917^(1/2))/2))*(x-((2917^(1/2)+1)/2)))/9 = 0 // * 9

3*(x-((1-2917^(1/2))/2))*(x-((2917^(1/2)+1)/2)) = 0

( x-((1-2917^(1/2))/2) )

x-((1-2917^(1/2))/2) = 0 // + (1-2917^(1/2))/2

x = (1-2917^(1/2))/2

( x-((2917^(1/2)+1)/2) )

x-((2917^(1/2)+1)/2) = 0 // + (2917^(1/2)+1)/2

x = (2917^(1/2)+1)/2

x in { (1-2917^(1/2))/2, (2917^(1/2)+1)/2 }

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