5k^2+3k-8=0

Solution for 5k^2+3k-8=0 equation:

Simplifying
5k2 + 3k + -8 = 0

Reorder the terms:
-8 + 3k + 5k2 = 0

Solving
-8 + 3k + 5k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-8 + -5k)(1 + -1k) = 0

Subproblem 1
Set the factor '(-8 + -5k)' equal to zero and attempt to solve:

Simplifying
-8 + -5k = 0

Solving
-8 + -5k = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5k = 0 + 8
-5k = 0 + 8

Combine like terms: 0 + 8 = 8
-5k = 8

Divide each side by '-5'.
k = -1.6

Simplifying
k = -1.6
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 = {-1.6, 1}