5x*x+12x+3=0

Solution for 5x*x+12x+3=0 equation:

Simplifying
5x * x + 12x + 3 = 0

Multiply x * x
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 = 0.84
1.44 + 2.4x + x2 = 0.84

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 0.84

Calculate the square root of the right side: 0.916515139

Break this problem into two subproblems by setting 
(x + 1.2) equal to 0.916515139 and -0.916515139.

Subproblem 1
x + 1.2 = 0.916515139

Simplifying
x + 1.2 = 0.916515139

Reorder the terms:
1.2 + x = 0.916515139

Solving
1.2 + x = 0.916515139

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 = 0.916515139 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 0.916515139 + -1.2
x = 0.916515139 + -1.2

Combine like terms: 0.916515139 + -1.2 = -0.283484861
x = -0.283484861

Simplifying
x = -0.283484861

Subproblem 2
x + 1.2 = -0.916515139

Simplifying
x + 1.2 = -0.916515139

Reorder the terms:
1.2 + x = -0.916515139

Solving
1.2 + x = -0.916515139

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 = -0.916515139 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -0.916515139 + -1.2
x = -0.916515139 + -1.2

Combine like terms: -0.916515139 + -1.2 = -2.116515139
x = -2.116515139

Simplifying
x = -2.116515139

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.283484861, -2.116515139}