Solve the inequality 2x^2+4x-7

We have to solve the inequality: 2x^2 + 4x - 7 <
0

2x^2 + 4x - 7 can be written as factors of roots
as

(x - x1)(x - x2), where

x1
= -4/4 + sqrt (16 + 56)/4

=> x1 = -1 + 6(sqrt
2)/4

=> x1 = -1 + (3*sqrt
2)/2

x2 = -1 - (3*sqrt 2)/2

As
a product of factors we have: (x - (-1 + (3*sqrt 2)/2))(x - (-1 - (3*sqrt
2)/2)

This is negative when either of (x - (-1 + (3*sqrt
2)/2)) or (x - (-1 - (3*sqrt 2)/2) is
negative.

• (x - (-1 + (3*sqrt 2)/2)) < 0
  and (x - (-1 - (3*sqrt 2)/2) >
  0

=> x < (-1 + (3*sqrt 2)/2) and
x > (-1 - (3*sqrt 2)/2). This gives the values of x in the interval ( (-1 -
(3*sqrt 2)/2), (-1 + (3*sqrt 2)/2).

• (x - (-1 +
  (3*sqrt 2)/2)) > 0 and (x - (-1 - (3*sqrt 2)/2) < 0
  

=> x > (-1 + (3*sqrt 2)/2) and x
< (-1 - (3*sqrt 2)/2) which is not
possible.

The solution for the inequality is
x in the range ((-1 - (3*sqrt 2)/2), (-1 + (3*sqrt
2)/2).