8k^2-31k-4=0

Solution for 8k^2-31k-4=0 equation:

Simplifying
8k2 + -31k + -4 = 0

Reorder the terms:
-4 + -31k + 8k2 = 0

Solving
-4 + -31k + 8k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-1 + -8k)(4 + -1k) = 0

Subproblem 1
Set the factor '(-1 + -8k)' equal to zero and attempt to solve:

Simplifying
-1 + -8k = 0

Solving
-1 + -8k = 0

Move all terms containing k to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -8k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8k = 0 + 1
-8k = 0 + 1

Combine like terms: 0 + 1 = 1
-8k = 1

Divide each side by '-8'.
k = -0.125

Simplifying
k = -0.125
Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-0.125, 4}