5k^2=-11k+114

Solution for 5k^2=-11k+114 equation:

Simplifying
5k2 = -11k + 114

Reorder the terms:
5k2 = 114 + -11k

Solving
5k2 = 114 + -11k

Solving for variable 'k'.

Reorder the terms:
-114 + 11k + 5k2 = 114 + -11k + -114 + 11k

Reorder the terms:
-114 + 11k + 5k2 = 114 + -114 + -11k + 11k

Combine like terms: 114 + -114 = 0
-114 + 11k + 5k2 = 0 + -11k + 11k
-114 + 11k + 5k2 = -11k + 11k

Combine like terms: -11k + 11k = 0
-114 + 11k + 5k2 = 0

Factor a trinomial.
(-6 + -1k)(19 + -5k) = 0

Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(19 + -5k)' equal to zero and attempt to solve:

Simplifying
19 + -5k = 0

Solving
19 + -5k = 0

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

Add '-19' to each side of the equation.
19 + -19 + -5k = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -5k = 0 + -19
-5k = 0 + -19

Combine like terms: 0 + -19 = -19
-5k = -19

Divide each side by '-5'.
k = 3.8

Simplifying
k = 3.8
Solution
k = {-6, 3.8}