(2x+5)/(-3x+1)=2x+5(-2)

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Solution for (2x+5)/(-3x+1)=2x+5(-2) equation:


D( x )

1-3*x = 0

1-3*x = 0

1-3*x = 0

1-3*x = 0 // - 1

-3*x = -1 // : -3

x = -1/(-3)

x = 1/3

x in (-oo:1/3) U (1/3:+oo)

(2*x+5)/(1-3*x) = 2*x-2*5 // - 2*x-2*5

(2*x+5)/(1-3*x)-(2*x)-(-2*5) = 0

(2*x+5)/(1-3*x)-2*x+10 = 0

(2*x+5)/(1-3*x)+(-2*x*(1-3*x))/(1-3*x)+(10*(1-3*x))/(1-3*x) = 0

10*(1-3*x)-2*x*(1-3*x)+2*x+5 = 0

6*x^2-30*x+5+10 = 0

6*x^2-30*x+15 = 0

6*x^2-30*x+15 = 0

3*(2*x^2-10*x+5) = 0

2*x^2-10*x+5 = 0

DELTA = (-10)^2-(2*4*5)

DELTA = 60

DELTA > 0

x = (60^(1/2)+10)/(2*2) or x = (10-60^(1/2))/(2*2)

x = (2*15^(1/2)+10)/4 or x = (10-2*15^(1/2))/4

3*(x-((10-2*15^(1/2))/4))*(x-((2*15^(1/2)+10)/4)) = 0

(3*(x-((10-2*15^(1/2))/4))*(x-((2*15^(1/2)+10)/4)))/(1-3*x) = 0

(3*(x-((10-2*15^(1/2))/4))*(x-((2*15^(1/2)+10)/4)))/(1-3*x) = 0 // * 1-3*x

3*(x-((10-2*15^(1/2))/4))*(x-((2*15^(1/2)+10)/4)) = 0

( x-((10-2*15^(1/2))/4) )

x-((10-2*15^(1/2))/4) = 0 // + (10-2*15^(1/2))/4

x = (10-2*15^(1/2))/4

( x-((2*15^(1/2)+10)/4) )

x-((2*15^(1/2)+10)/4) = 0 // + (2*15^(1/2)+10)/4

x = (2*15^(1/2)+10)/4

x in { (10-2*15^(1/2))/4, (2*15^(1/2)+10)/4 }

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