8q^2-18q-5=0

Solution for 8q^2-18q-5=0 equation:

Simplifying
8q2 + -18q + -5 = 0

Reorder the terms:
-5 + -18q + 8q2 = 0

Solving
-5 + -18q + 8q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-1 + -4q)(5 + -2q) = 0

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

Simplifying
-1 + -4q = 0

Solving
-1 + -4q = 0

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

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

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

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

Divide each side by '-4'.
q = -0.25

Simplifying
q = -0.25
Subproblem 2
Set the factor '(5 + -2q)' equal to zero and attempt to solve:

Simplifying
5 + -2q = 0

Solving
5 + -2q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2q = 0 + -5
-2q = 0 + -5

Combine like terms: 0 + -5 = -5
-2q = -5

Divide each side by '-2'.
q = 2.5

Simplifying
q = 2.5
Solution
q = {-0.25, 2.5}