5k^2-2k-7=0

Solution for 5k^2-2k-7=0 equation:

Simplifying
5k2 + -2k + -7 = 0

Reorder the terms:
-7 + -2k + 5k2 = 0

Solving
-7 + -2k + 5k2 = 0

Solving for variable 'k'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -5k)' equal to zero and attempt to solve:

Simplifying
7 + -5k = 0

Solving
7 + -5k = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5k = 0 + -7

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

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

Divide each side by '-5'.
k = 1.4

Simplifying
k = 1.4
Solution
k = {-1, 1.4}