Step 1: Note-down the given quadratic equation and compare it with the standard form ax^2 + bx + c

EXAMPLE: 2x^2 - 3x - (k+1)

                   ax^2 + bx + c

Where a = 2, b = -3 and c = -(k+1)

Step 2: Look the hints given in the question according to that hints choose the discrimination( b^2-4ac ) of the equation.

HINTS:1) b^2 - 4ac > 0 (Positive), there are 2 real solutions

          2) b^2-4ac = 0 (Zero), there is one real solution

          3) b^2-4ac < 0 (Negative), there are 2 complex solutions or no real roots.

EXAMPLE: HINT: Has no real roots

So we have to take the discrimination of b^2-4ac < 0

Step 3: Substitute all the values of a, b and c in the suitable discrimination.

EXAMPLE: [math] (-3)^2 - 4 [2][-(k+1)] < 0[/math]

Step 4: Simplify the inequality to find the unknown value.

NOTE: Apply inverse operations on both sides

EXAMPLE: 9 + 8k + 8 <0

                  8k+17<0

                    8k < -17

                 k\ <\ \frac{-17}{8}