How Do You Solve for x Given the Determinant of a Matrix?

[Nile3]

Find the value of x when the matrix equals 3:

|x-2 3|
|x x+1|

so I find the determinant:
(x-2)(x+1)-(x)(3)
x^2-4x-2

How do I find which values are giving 3 from here?

 

[vela]

Find the value of x when the matrix equals 3:

You mean when the determinant of the matrix equals 3. The matrix doesn't equal 3.

You found
$$\begin{vmatrix} x-2 & 3 \\ x & x+1 \end{vmatrix} = x^2-4x-2$$ so set that expression equal to 3 and solve for x.