7k^2=6k+1

Solution for 7k^2=6k+1 equation:

Simplifying
7k2 = 6k + 1

Reorder the terms:
7k2 = 1 + 6k

Solving
7k2 = 1 + 6k

Solving for variable 'k'.

Reorder the terms:
-1 + -6k + 7k2 = 1 + 6k + -1 + -6k

Reorder the terms:
-1 + -6k + 7k2 = 1 + -1 + 6k + -6k

Combine like terms: 1 + -1 = 0
-1 + -6k + 7k2 = 0 + 6k + -6k
-1 + -6k + 7k2 = 6k + -6k

Combine like terms: 6k + -6k = 0
-1 + -6k + 7k2 = 0

Factor a trinomial.
(-1 + -7k)(1 + -1k) = 0

Subproblem 1
Set the factor '(-1 + -7k)' equal to zero and attempt to solve:

Simplifying
-1 + -7k = 0

Solving
-1 + -7k = 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 + -7k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7k = 0 + 1
-7k = 0 + 1

Combine like terms: 0 + 1 = 1
-7k = 1

Divide each side by '-7'.
k = -0.1428571429

Simplifying
k = -0.1428571429
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

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

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

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

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

Simplifying
k = 1
Solution
k = {-0.1428571429, 1}