What is 3x^2+5x-2-x^2+10x-25>0 ?

The solution to 3x^2+5x-2-x^2+10x-25>0 is x 3/2

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3x^2+5x-2-x^2+10x-25>0

3 x^{2} + 5 x - 2 - x^{2} + 10 x - 25 > 0

x < - 9 or x > \frac{3}{2}

Interval Notation

(- \infty, - 9) \cup (\frac{3}{2}, \infty)

Decimal Notation

x < - 9 or x > 1.5

Solution steps

3 x^{2} + 5 x - 2 - x^{2} + 10 x - 25 > 0

Rewrite in standard form

2 x^{2} + 15 x - 27 > 0

Factor

2 x^{2} + 15 x - 27 : (2 x - 3) (x + 9)

(2 x - 3) (x + 9) > 0

Identify the intervals

x < - 9 or x > \frac{3}{2}

(a - 1)^{2} (a + 1) > 0

x (x + 6) \cdot (x + 2)^{2} \cdot (x - 3) > 0

\frac{1}{x} > \frac{1}{x} + 1

(x^{2} + 1) (x - 1) (x - 2) < 0

\frac{1}{( x - 1 )} - \frac{1}{( x - 2 )} + \frac{1}{( x - 3 )} > 0

What is 3x^2+5x-2-x^2+10x-25>0 ?
The solution to 3x^2+5x-2-x^2+10x-25>0 is x<-9\lor x> 3/2