3K^2-38K-13=0

Solution for 3K^2-38K-13=0 equation:

Simplifying
3K2 + -38K + -13 = 0

Reorder the terms:
-13 + -38K + 3K2 = 0

Solving
-13 + -38K + 3K2 = 0

Solving for variable 'K'.

Factor a trinomial.
(-1 + -3K)(13 + -1K) = 0

Subproblem 1
Set the factor '(-1 + -3K)' equal to zero and attempt to solve:

Simplifying
-1 + -3K = 0

Solving
-1 + -3K = 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 + -3K = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3K = 0 + 1
-3K = 0 + 1

Combine like terms: 0 + 1 = 1
-3K = 1

Divide each side by '-3'.
K = -0.3333333333

Simplifying
K = -0.3333333333
Subproblem 2
Set the factor '(13 + -1K)' equal to zero and attempt to solve:

Simplifying
13 + -1K = 0

Solving
13 + -1K = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1K = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1K = 0 + -13
-1K = 0 + -13

Combine like terms: 0 + -13 = -13
-1K = -13

Divide each side by '-1'.
K = 13

Simplifying
K = 13
Solution
K = {-0.3333333333, 13}