What is 3x(x-2)>1-7x-3x^2 ?

The solution to 3x(x-2)>1-7x-3x^2 is x 1/3

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3x(x-2)>1-7x-3x^2

3 x (x - 2) > 1 - 7 x - 3 x^{2}

x < - \frac{1}{2} or x > \frac{1}{3}

Interval Notation

(- \infty, - \frac{1}{2}) \cup (\frac{1}{3}, \infty)

Decimal Notation

x < - 0.5 or x > 0.33333 \dots

Solution steps

3 x (x - 2) > 1 - 7 x - 3 x^{2}

Rewrite in standard form

6 x^{2} + x - 1 > 0

Factor

6 x^{2} + x - 1 : (3 x - 1) (2 x + 1)

(3 x - 1) (2 x + 1) > 0

Identify the intervals

x < - \frac{1}{2} or x > \frac{1}{3}

\frac{x + 2}{15} - \frac{x - 3}{5} = \frac{2}{3}

\frac{5}{( 7 - 2 x )} > 0

x^{2} = (x + 6) (x - 6) + 36

(x - 2) (x + 3) = 14

\frac{16}{5}

What is 3x(x-2)>1-7x-3x^2 ?
The solution to 3x(x-2)>1-7x-3x^2 is x<-1/2 \lor x> 1/3