-5x^2-12x+3=0

Solution for -5x^2-12x+3=0 equation:

Simplifying
-5x2 + -12x + 3 = 0

Reorder the terms:
3 + -12x + -5x2 = 0

Solving
3 + -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'.
-0.6 + 2.4x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 2.4x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 2.4x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 2.4x + x2 = 0 + 0.6
2.4x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
2.4x + x2 = 0.6

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 = 0.6 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 0.6 + 1.44

Combine like terms: 0.6 + 1.44 = 2.04
1.44 + 2.4x + x2 = 2.04

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 2.04

Calculate the square root of the right side: 1.428285686

Break this problem into two subproblems by setting 
(x + 1.2) equal to 1.428285686 and -1.428285686.

Subproblem 1
x + 1.2 = 1.428285686

Simplifying
x + 1.2 = 1.428285686

Reorder the terms:
1.2 + x = 1.428285686

Solving
1.2 + x = 1.428285686

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 = 1.428285686 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 1.428285686 + -1.2
x = 1.428285686 + -1.2

Combine like terms: 1.428285686 + -1.2 = 0.228285686
x = 0.228285686

Simplifying
x = 0.228285686

Subproblem 2
x + 1.2 = -1.428285686

Simplifying
x + 1.2 = -1.428285686

Reorder the terms:
1.2 + x = -1.428285686

Solving
1.2 + x = -1.428285686

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 = -1.428285686 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -1.428285686 + -1.2
x = -1.428285686 + -1.2

Combine like terms: -1.428285686 + -1.2 = -2.628285686
x = -2.628285686

Simplifying
x = -2.628285686

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.228285686, -2.628285686}