5x^2+12x-1=0

Solution for 5x^2+12x-1=0 equation:

Simplifying
5x2 + 12x + -1 = 0

Reorder the terms:
-1 + 12x + 5x2 = 0

Solving
-1 + 12x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.2 + 2.4x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 2.4x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 2.4x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 2.4x + x2 = 0 + 0.2
2.4x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
2.4x + x2 = 0.2

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 0.2 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 0.2 + 1.44

Combine like terms: 0.2 + 1.44 = 1.64
1.44 + 2.4x + x2 = 1.64

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(x + 1.2) equal to 1.280624847 and -1.280624847.

Subproblem 1
x + 1.2 = 1.280624847

Simplifying
x + 1.2 = 1.280624847

Reorder the terms:
1.2 + x = 1.280624847

Solving
1.2 + x = 1.280624847

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = 1.280624847 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 1.280624847 + -1.2
x = 1.280624847 + -1.2

Combine like terms: 1.280624847 + -1.2 = 0.080624847
x = 0.080624847

Simplifying
x = 0.080624847

Subproblem 2
x + 1.2 = -1.280624847

Simplifying
x + 1.2 = -1.280624847

Reorder the terms:
1.2 + x = -1.280624847

Solving
1.2 + x = -1.280624847

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = -1.280624847 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -1.280624847 + -1.2
x = -1.280624847 + -1.2

Combine like terms: -1.280624847 + -1.2 = -2.480624847
x = -2.480624847

Simplifying
x = -2.480624847

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.080624847, -2.480624847}