(3x^2+x-14)/(2x^2-11+5)*(2x-1)/(3x-6)

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Solution for (3x^2+x-14)/(2x^2-11+5)*(2x-1)/(3x-6) equation:


D( x )

2*x^2-11+5 = 0

3*x-6 = 0

2*x^2-11+5 = 0

2*x^2-11+5 = 0

2*x^2 = 6 // : 2

x^2 = 3

x^2 = 3 // ^ 1/2

abs(x) = 3^(1/2)

x = 3^(1/2) or x = -3^(1/2)

3*x-6 = 0

3*x-6 = 0

3*x-6 = 0 // + 6

3*x = 6 // : 3

x = 6/3

x = 2

x in (-oo:-3^(1/2)) U (-3^(1/2):3^(1/2)) U (3^(1/2):2) U (2:+oo)

(((3*x^2+x-14)/(2*x^2-11+5))*(2*x-1))/(3*x-6) = 0

((3*x^2+x-14)*(2*x-1))/((2*x^2-6)*(3*x-6)) = 0

3*x^2+x-14 = 0

3*x^2+x-14 = 0

DELTA = 1^2-(-14*3*4)

DELTA = 169

DELTA > 0

x = (169^(1/2)-1)/(2*3) or x = (-169^(1/2)-1)/(2*3)

x = 2 or x = -7/3

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

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

( 2*x-1 )

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

( x+7/3 )

x+7/3 = 0 // - 7/3

x = -7/3

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 2}

x in { 1/2, -7/3 }

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