5q^2-4q-1=0

Solution for 5q^2-4q-1=0 equation:

Simplifying
5q2 + -4q + -1 = 0

Reorder the terms:
-1 + -4q + 5q2 = 0

Solving
-1 + -4q + 5q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-1 + -5q = 0

Solving
-1 + -5q = 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 + -5q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5q = 0 + 1
-5q = 0 + 1

Combine like terms: 0 + 1 = 1
-5q = 1

Divide each side by '-5'.
q = -0.2

Simplifying
q = -0.2
Subproblem 2
Set the factor '(1 + -1q)' equal to zero and attempt to solve:

Simplifying
1 + -1q = 0

Solving
1 + -1q = 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 + -1q = 0 + -1

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

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

Divide each side by '-1'.
q = 1

Simplifying
q = 1
Solution
q = {-0.2, 1}