Roots of Quadratic Equations - The Discriminant

Hi, I am just on the Roots of Quadratics section and I have been trying to get my head round this example but I just can't figure it out.

I think there is a chance it could of been badly written but would someone please be able to walk me through from start to finish and tell me where the '>' sign came from.

Here is the example written as is. Spacings and everything.

Thanks very much in advance :^]

Example 1

For what range of values of k does the equation x^2+(2k+1)x+(k+1) = 0, have 2 real unequal roots?

Discriminant. = (2k + 1)2 - 4(k+1) > 0
4k^2 - 3 > 0

We draw the graph of y = 4k^2 - 3

*The graph drawn shows x @ '-√3/4' and '√3/4' and the vertex on y @ -3'

Can someone please walk me through this example?
How was the >0 and the '-√3/4' and '√3/4' worked out?

Thanks very much,
And the

Discriminant. = (2k + 1)^2 - 4(k+1) > 0
4k^2 - 3 > 0

Is that just expansion of the brackets?

The discriminant is $b^2-4ac$

Thank you for your help! and how would I go about getting from

x^2 + (2k+1) + (k+1) = 0
to
= (2k+1)2 - 4(k+1) > 0

what model should I be following?