−2x2+5x+12<0-2{x}^{2}+5x+12<0
1
Multiply both sides by −1-1.
2x2−5x−12>02{x}^{2}-5x-12>0

2
Split the second term in 2x2−5x−122{x}^{2}-5x-12 into two terms.
2x2+3x−8x−12>02{x}^{2}+3x-8x-12>0

3
Factor out common terms in the first two terms, then in the last two terms.
x(2x+3)−4(2x+3)>0x(2x+3)-4(2x+3)>0

4
Factor out the common term 2x+32x+3.
(2x+3)(x−4)>0(2x+3)(x-4)>0

5
Solve for xx.
x=−32,4x=-\frac{3}{2},4

6
From the values of xx above, we have these 3 intervals to test.
x<−32−32<x<4x>4\begin{aligned}&x<-\frac{3}{2}\\&-\frac{3}{2}<x<4\\&x>4\end{aligned}

7
Pick a test point for each interval.
For the interval x<−32x<-\frac{3}{2}:

Let's pick x=−2x=-2. Then, −2(−2)2+5×−2+12<0-2{(-2)}^{2}+5\times -2+12<0.
After simplifying, we get −6<0-6<0, which is
true
.
Keep this interval.
.

For the interval −32<x<4-\frac{3}{2}<x<4:

Let's pick x=0x=0. Then, −2×02+5×0+12<0-2\times {0}^{2}+5\times 0+12<0.
After simplifying, we get 12<012<0, which is
false
.
Drop this interval.
.

For the interval x>4x>4:

Let's pick x=5x=5. Then, −2×52+5×5+12<0-2\times {5}^{2}+5\times 5+12<0.
After simplifying, we get −13<0-13<0, which is
true
.
Keep this interval.
.

8
Therefore,
x<−32,x>4x<-\frac{3}{2},x>4

Done
Copy Link
How can we make this solution more helpful?
Cymath foriOSAndroid