6x^2+3x-2=

Solution for 6x^2+3x-2= equation:

Simplifying
6x2 + 3x + -2 = 0

Reorder the terms:
-2 + 3x + 6x2 = 0

Solving
-2 + 3x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.3333333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.5x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.5x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.5x + x2 = 0 + 0.3333333333
0.5x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.5x + x2 = 0.3333333333

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.3333333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.3333333333 + 0.0625

Combine like terms: 0.3333333333 + 0.0625 = 0.3958333333
0.0625 + 0.5x + x2 = 0.3958333333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.3958333333

Calculate the square root of the right side: 0.62915287

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.62915287 and -0.62915287.

Subproblem 1
x + 0.25 = 0.62915287

Simplifying
x + 0.25 = 0.62915287

Reorder the terms:
0.25 + x = 0.62915287

Solving
0.25 + x = 0.62915287

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.62915287 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.62915287 + -0.25
x = 0.62915287 + -0.25

Combine like terms: 0.62915287 + -0.25 = 0.37915287
x = 0.37915287

Simplifying
x = 0.37915287

Subproblem 2
x + 0.25 = -0.62915287

Simplifying
x + 0.25 = -0.62915287

Reorder the terms:
0.25 + x = -0.62915287

Solving
0.25 + x = -0.62915287

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.62915287 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.62915287 + -0.25
x = -0.62915287 + -0.25

Combine like terms: -0.62915287 + -0.25 = -0.87915287
x = -0.87915287

Simplifying
x = -0.87915287

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.37915287, -0.87915287}