5n^2+7n-34=0

Solution for 5n^2+7n-34=0 equation:

Simplifying
5n2 + 7n + -34 = 0

Reorder the terms:
-34 + 7n + 5n2 = 0

Solving
-34 + 7n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-17 + -5n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-17 + -5n)' equal to zero and attempt to solve:

Simplifying
-17 + -5n = 0

Solving
-17 + -5n = 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 + -5n = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -5n = 0 + 17
-5n = 0 + 17

Combine like terms: 0 + 17 = 17
-5n = 17

Divide each side by '-5'.
n = -3.4

Simplifying
n = -3.4
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 = {-3.4, 2}