(3x-1)/4x-9=5/7

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Solution for (3x-1)/4x-9=5/7 equation:


x in (-oo:+oo)

x*((3*x-1)/4)-9 = 5/7 // - 5/7

x*((3*x-1)/4)-(5/7)-9 = 0

x*((3*x-1)/4)-5/7-9 = 0

(x*(3*x-1))/4-5/7-9 = 0

(7*x*(3*x-1))/(4*7)+(-5*4)/(4*7)+(-9*4*7)/(4*7) = 0

7*x*(3*x-1)-5*4-9*4*7 = 0

21*x^2-7*x-252-20 = 0

21*x^2-7*x-272 = 0

21*x^2-7*x-272 = 0

21*x^2-7*x-272 = 0

DELTA = (-7)^2-(-272*4*21)

DELTA = 22897

DELTA > 0

x = (22897^(1/2)+7)/(2*21) or x = (7-22897^(1/2))/(2*21)

x = (22897^(1/2)+7)/42 or x = (7-22897^(1/2))/42

(x-((7-22897^(1/2))/42))*(x-((22897^(1/2)+7)/42)) = 0

((x-((7-22897^(1/2))/42))*(x-((22897^(1/2)+7)/42)))/(4*7) = 0

((x-((7-22897^(1/2))/42))*(x-((22897^(1/2)+7)/42)))/(4*7) = 0 // * 4*7

(x-((7-22897^(1/2))/42))*(x-((22897^(1/2)+7)/42)) = 0

( x-((22897^(1/2)+7)/42) )

x-((22897^(1/2)+7)/42) = 0 // + (22897^(1/2)+7)/42

x = (22897^(1/2)+7)/42

( x-((7-22897^(1/2))/42) )

x-((7-22897^(1/2))/42) = 0 // + (7-22897^(1/2))/42

x = (7-22897^(1/2))/42

x in { (22897^(1/2)+7)/42, (7-22897^(1/2))/42 }

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