8n^2+n-34=0

Solution for 8n^2+n-34=0 equation:

Simplifying
8n2 + n + -34 = 0

Reorder the terms:
-34 + n + 8n2 = 0

Solving
-34 + n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-17 + -8n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-17 + -8n)' equal to zero and attempt to solve:

Simplifying
-17 + -8n = 0

Solving
-17 + -8n = 0

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

Add '17' to each side of the equation.
-17 + 17 + -8n = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -8n = 0 + 17
-8n = 0 + 17

Combine like terms: 0 + 17 = 17
-8n = 17

Divide each side by '-8'.
n = -2.125

Simplifying
n = -2.125
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-2.125, 2}