Verified answer

Factorize to get (3x + 1)(x - 5) < 0

The graph of y = (3x + 1)(x - 5) is a parabola that cuts the x axis at ( -1/3, 0 ) and (5 , 0) and it is below

the x axis between -1/3 and 5 hence y = (3x+1)(x - 5) < 0 when -1/3 < x < 5.

Dear;

assume 3x^2-14x-5=0

then delta = 14^2-4*3*(-5)=256 ---> delta ^.5 =16

so roots of the equation are :

x= (14-16)/2*3=-2/6 =-1/3

and

x=(14+16)/(2*3)=30/6=5

Now we reach to the moment of solving 3x2 −14x−5<0

Always if you have equation ax^2+bx+c=0 with roots X1, X2 then

between X1 and X2 the value is opposite of a in ( ax^2+bx+c=0 ).

in our case X1=-1/3 , X2=5 , our equation 3x2 −14x−5=0 so a=3 >0

for this

x<X1 --->> x<-1/3 ----> 3x2 −14x−5>0

X1<x<X2 --->> 3x2 −14x−5<0

x>X2 --->> x>5 ----> 3x2 −14x−5>0

Always after solving take an example to check if your work is correct.

if x=0 --->>> 3x2 −14x−5<0 ---->>> 0-0-5 <0 ---->>> correct -5<0

Good luck

The answer that you know is wrong because:

3*2 - 14x - 5<0

6-14x-5<0

1-14x<0

14x>1

So, x>1/14 (Ans.)

you can substitute numbers between -1/3 and 5 from x and the result is less than zero