7k^2=5-34k

Solution for 7k^2=5-34k equation:

Simplifying
7k2 = 5 + -34k

Solving
7k2 = 5 + -34k

Solving for variable 'k'.

Reorder the terms:
-5 + 34k + 7k2 = 5 + -34k + -5 + 34k

Reorder the terms:
-5 + 34k + 7k2 = 5 + -5 + -34k + 34k

Combine like terms: 5 + -5 = 0
-5 + 34k + 7k2 = 0 + -34k + 34k
-5 + 34k + 7k2 = -34k + 34k

Combine like terms: -34k + 34k = 0
-5 + 34k + 7k2 = 0

Factor a trinomial.
(-5 + -1k)(1 + -7k) = 0

Subproblem 1
Set the factor '(-5 + -1k)' equal to zero and attempt to solve:

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -5
Subproblem 2
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
Solution
k = {-5, 0.1428571429}