3x+7=4/(5-2x)

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Solution for 3x+7=4/(5-2x) equation:


D( x )

5-(2*x) = 0

5-(2*x) = 0

5-(2*x) = 0

5-2*x = 0

5-2*x = 0 // - 5

-2*x = -5 // : -2

x = -5/(-2)

x = 5/2

x in (-oo:5/2) U (5/2:+oo)

3*x+7 = 4/(5-(2*x)) // - 4/(5-(2*x))

3*x-(4/(5-(2*x)))+7 = 0

3*x-4*(5-2*x)^-1+7 = 0

3*x-4/(5-2*x)+7 = 0

(3*x*(5-2*x))/(5-2*x)-4/(5-2*x)+(7*(5-2*x))/(5-2*x) = 0

3*x*(5-2*x)+7*(5-2*x)-4 = 0

15*x-6*x^2-14*x-4+35 = 0

x-6*x^2+31 = 0

x-6*x^2+31 = 0

x-6*x^2+31 = 0

DELTA = 1^2-(-6*4*31)

DELTA = 745

DELTA > 0

x = (745^(1/2)-1)/(-6*2) or x = (-745^(1/2)-1)/(-6*2)

x = (745^(1/2)-1)/(-12) or x = (745^(1/2)+1)/12

(x-((745^(1/2)-1)/(-12)))*(x-((745^(1/2)+1)/12)) = 0

((x-((745^(1/2)-1)/(-12)))*(x-((745^(1/2)+1)/12)))/(5-2*x) = 0

((x-((745^(1/2)-1)/(-12)))*(x-((745^(1/2)+1)/12)))/(5-2*x) = 0 // * 5-2*x

(x-((745^(1/2)-1)/(-12)))*(x-((745^(1/2)+1)/12)) = 0

( x-((745^(1/2)+1)/12) )

x-((745^(1/2)+1)/12) = 0 // + (745^(1/2)+1)/12

x = (745^(1/2)+1)/12

( x-((745^(1/2)-1)/(-12)) )

x-((745^(1/2)-1)/(-12)) = 0 // + (745^(1/2)-1)/(-12)

x = (745^(1/2)-1)/(-12)

x in { (745^(1/2)+1)/12, (745^(1/2)-1)/(-12) }

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