(3x^2-4x-7)/(2x^2-6x)=1

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Solution for (3x^2-4x-7)/(2x^2-6x)=1 equation: 


D( x )

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

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

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

2*x^2-6*x = 0

2*x^2-6*x = 0

DELTA = (-6)^2-(0*2*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)+6)/(2*2) or x = (6-36^(1/2))/(2*2)

x = 3 or x = 0

x in (-oo:0) U (0:3) U (3:+oo)

(3*x^2-(4*x)-7)/(2*x^2-(6*x)) = 1 // - 1

(3*x^2-(4*x)-7)/(2*x^2-(6*x))-1 = 0

(3*x^2-4*x-7)/(2*x^2-6*x)-1 = 0

2*x^2-6*x = 0

2*x^2-6*x = 0

2*x*(x-3) = 0

x-3 = 0 // + 3

x = 3

2*x*(x-3) = 0

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

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

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

x^2+2*x-7 = 0

x^2+2*x-7 = 0

x^2+2*x-7 = 0

DELTA = 2^2-(-7*1*4)

DELTA = 32

DELTA > 0

x = (32^(1/2)-2)/(1*2) or x = (-32^(1/2)-2)/(1*2)

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

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

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

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

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

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

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

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

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

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

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

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

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