-5s^2+15s+1=0

Solution for -5s^2+15s+1=0 equation:

Simplifying
-5s2 + 15s + 1 = 0

Reorder the terms:
1 + 15s + -5s2 = 0

Solving
1 + 15s + -5s2 = 0

Solving for variable 's'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.2 + -3s + s2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -3s + 0.2 + s2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -3s + s2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -3s + s2 = 0 + 0.2
-3s + s2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-3s + s2 = 0.2

The s term is -3s.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3s + 2.25 + s2 = 0.2 + 2.25

Reorder the terms:
2.25 + -3s + s2 = 0.2 + 2.25

Combine like terms: 0.2 + 2.25 = 2.45
2.25 + -3s + s2 = 2.45

Factor a perfect square on the left side:
(s + -1.5)(s + -1.5) = 2.45

Calculate the square root of the right side: 1.565247584

Break this problem into two subproblems by setting 
(s + -1.5) equal to 1.565247584 and -1.565247584.

Subproblem 1
s + -1.5 = 1.565247584

Simplifying
s + -1.5 = 1.565247584

Reorder the terms:
-1.5 + s = 1.565247584

Solving
-1.5 + s = 1.565247584

Solving for variable 's'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + s = 1.565247584 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = 1.565247584 + 1.5
s = 1.565247584 + 1.5

Combine like terms: 1.565247584 + 1.5 = 3.065247584
s = 3.065247584

Simplifying
s = 3.065247584

Subproblem 2
s + -1.5 = -1.565247584

Simplifying
s + -1.5 = -1.565247584

Reorder the terms:
-1.5 + s = -1.565247584

Solving
-1.5 + s = -1.565247584

Solving for variable 's'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + s = -1.565247584 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = -1.565247584 + 1.5
s = -1.565247584 + 1.5

Combine like terms: -1.565247584 + 1.5 = -0.065247584
s = -0.065247584

Simplifying
s = -0.065247584

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {3.065247584, -0.065247584}