What is ((3x^2-4x-6))/((2x-5))<0 ?

The solution to ((3x^2-4x-6))/((2x-5))<0 is x<(2-sqrt(22))/3 \lor (2+sqrt(22))/3 <x< 5/2

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((3x^2-4x-6))/((2x-5))<0

\frac{( 3 x ^{2} - 4 x - 6 )}{( 2 x - 5 )} < 0

x < \frac{2 - 22}{3} or \frac{2 + 22}{3} < x < \frac{5}{2}

Interval Notation

(- \infty, \frac{2 - 22}{3}) \cup (\frac{2 + 22}{3}, \frac{5}{2})

Decimal Notation

x < - 0.89680 \dots or 2.23013 \dots < x < 2.5

Solution steps

\frac{3 x ^{2} - 4 x - 6}{2 x - 5} < 0

Factor

3 x^{2} - 4 x - 6 : (x - \frac{2 + 22}{3}) (x - \frac{2 - 22}{3})

\frac{( x - \frac{2 + 22}{3} ) ( x - \frac{2 - 22}{3} )}{2 x - 5} < 0

Identify the intervals

x < \frac{2 - 22}{3} or \frac{2 + 22}{3} < x < \frac{5}{2}

\frac{( x ^{2} - 7 x + 12 )}{( 2 x ^{2} + 4 x + 5 )} > \frac{1}{2}

\frac{( x ^{4} )}{( ( x - 2 ) ^{2} )} > 0

\frac{( ( x - 1 ) ( x - 5 ) )}{( x - 3 )} > 0

\frac{1}{( x - x ^{2} - 1 )} < 0

\frac{1}{x} < \frac{2}{( x - 2 )}

What is ((3x^2-4x-6))/((2x-5))<0 ?
The solution to ((3x^2-4x-6))/((2x-5))<0 is x<(2-sqrt(22))/3 \lor (2+sqrt(22))/3 <x< 5/2