5a^2-9a-116=0

Solution for 5a^2-9a-116=0 equation:

Simplifying
5a2 + -9a + -116 = 0

Reorder the terms:
-116 + -9a + 5a2 = 0

Solving
-116 + -9a + 5a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-4 + -1a)(29 + -5a) = 0

Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(29 + -5a)' equal to zero and attempt to solve:

Simplifying
29 + -5a = 0

Solving
29 + -5a = 0

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

Add '-29' to each side of the equation.
29 + -29 + -5a = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -5a = 0 + -29
-5a = 0 + -29

Combine like terms: 0 + -29 = -29
-5a = -29

Divide each side by '-5'.
a = 5.8

Simplifying
a = 5.8
Solution
a = {-4, 5.8}