6k^2=3+17k

Solution for 6k^2=3+17k equation:

Simplifying
6k2 = 3 + 17k

Solving
6k2 = 3 + 17k

Solving for variable 'k'.

Reorder the terms:
-3 + -17k + 6k2 = 3 + 17k + -3 + -17k

Reorder the terms:
-3 + -17k + 6k2 = 3 + -3 + 17k + -17k

Combine like terms: 3 + -3 = 0
-3 + -17k + 6k2 = 0 + 17k + -17k
-3 + -17k + 6k2 = 17k + -17k

Combine like terms: 17k + -17k = 0
-3 + -17k + 6k2 = 0

Factor a trinomial.
(-1 + -6k)(3 + -1k) = 0

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

Simplifying
-1 + -6k = 0

Solving
-1 + -6k = 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 + -6k = 0 + 1

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

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

Divide each side by '-6'.
k = -0.1666666667

Simplifying
k = -0.1666666667
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {-0.1666666667, 3}