-5x^2+14x-6=0

Solution for -5x^2+14x-6=0 equation:

Simplifying
-5x2 + 14x + -6 = 0

Reorder the terms:
-6 + 14x + -5x2 = 0

Solving
-6 + 14x + -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'.
1.2 + -2.8x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -2.8x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -2.8x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -2.8x + x2 = 0 + -1.2
-2.8x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-2.8x + x2 = -1.2

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = -1.2 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = -1.2 + 1.96

Combine like terms: -1.2 + 1.96 = 0.76
1.96 + -2.8x + x2 = 0.76

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 0.76

Calculate the square root of the right side: 0.871779789

Break this problem into two subproblems by setting 
(x + -1.4) equal to 0.871779789 and -0.871779789.

Subproblem 1
x + -1.4 = 0.871779789

Simplifying
x + -1.4 = 0.871779789

Reorder the terms:
-1.4 + x = 0.871779789

Solving
-1.4 + x = 0.871779789

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = 0.871779789 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = 0.871779789 + 1.4
x = 0.871779789 + 1.4

Combine like terms: 0.871779789 + 1.4 = 2.271779789
x = 2.271779789

Simplifying
x = 2.271779789

Subproblem 2
x + -1.4 = -0.871779789

Simplifying
x + -1.4 = -0.871779789

Reorder the terms:
-1.4 + x = -0.871779789

Solving
-1.4 + x = -0.871779789

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = -0.871779789 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = -0.871779789 + 1.4
x = -0.871779789 + 1.4

Combine like terms: -0.871779789 + 1.4 = 0.528220211
x = 0.528220211

Simplifying
x = 0.528220211

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.271779789, 0.528220211}