52s^2-22s-2=0

Solution for 52s^2-22s-2=0 equation:

Simplifying
52s2 + -22s + -2 = 0

Reorder the terms:
-2 + -22s + 52s2 = 0

Solving
-2 + -22s + 52s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -11s + 26s2) = 0

Factor a trinomial.
2((-1 + -13s)(1 + -2s)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -13s)' equal to zero and attempt to solve:

Simplifying
-1 + -13s = 0

Solving
-1 + -13s = 0

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

Add '1' to each side of the equation.
-1 + 1 + -13s = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -13s = 0 + 1
-13s = 0 + 1

Combine like terms: 0 + 1 = 1
-13s = 1

Divide each side by '-13'.
s = -0.07692307692

Simplifying
s = -0.07692307692
Subproblem 2
Set the factor '(1 + -2s)' equal to zero and attempt to solve:

Simplifying
1 + -2s = 0

Solving
1 + -2s = 0

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

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

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

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

Divide each side by '-2'.
s = 0.5

Simplifying
s = 0.5
Solution
s = {-0.07692307692, 0.5}