Explain what are x values for the inequality 2x^2-7x+3

If we'll draw the graph of the function it will be a
concave upward parabola. The vertex of parabola is aminimum
point.

f(x) = 2x^2-7x+3

The
area between the roots of quadratic is the area where parabola goes below the x axis.
This area represents the solution of the inequality.

First,
we'll determine the roots of the quadratic:

2x^2-7x+3 =
0

We'll apply the quadratic
formula:

x1 = [7+sqrt(49 -
24)]/4

x1 = (7+sqrt25)/4

x1 =
(7+5)/4

x1 = 3

x2 =
(7-5)/4

x2 =
1/2

The expression
2x^2-7x+3 is negative when x
belongs to the range  (1/2 ; 3).