(x-(4/9))(x-(4/9))=70/81

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Solution for (x-(4/9))(x-(4/9))=70/81 equation: 


x in (-oo:+oo)

(x-(4/9))*(x-(4/9)) = 70/81 // - 70/81

(x-(4/9))*(x-(4/9))-(70/81) = 0

(x-4/9)*(x-4/9)-70/81 = 0

(x-4/9)^2-70/81 = 0

(81*(x-4/9)^2)/81-70/81 = 0

81*(x-4/9)^2-70 = 0

81*x^2-72*x-54 = 0

81*x^2-72*x-54 = 0

9*(9*x^2-8*x-6) = 0

9*x^2-8*x-6 = 0

DELTA = (-8)^2-(-6*4*9)

DELTA = 280

DELTA > 0

x = (280^(1/2)+8)/(2*9) or x = (8-280^(1/2))/(2*9)

x = (2*70^(1/2)+8)/18 or x = (8-2*70^(1/2))/18

9*(x-((8-2*70^(1/2))/18))*(x-((2*70^(1/2)+8)/18)) = 0

(9*(x-((8-2*70^(1/2))/18))*(x-((2*70^(1/2)+8)/18)))/81 = 0

(9*(x-((8-2*70^(1/2))/18))*(x-((2*70^(1/2)+8)/18)))/81 = 0 // * 81

9*(x-((8-2*70^(1/2))/18))*(x-((2*70^(1/2)+8)/18)) = 0

( 9 )

9 = 0

x belongs to the empty set

( x-((2*70^(1/2)+8)/18) )

x-((2*70^(1/2)+8)/18) = 0 // + (2*70^(1/2)+8)/18

x = (2*70^(1/2)+8)/18

( x-((8-2*70^(1/2))/18) )

x-((8-2*70^(1/2))/18) = 0 // + (8-2*70^(1/2))/18

x = (8-2*70^(1/2))/18

x in { (2*70^(1/2)+8)/18, (8-2*70^(1/2))/18 }

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