5x^2-6+14x=0

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

Simplifying
5x2 + -6 + 14x = 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 = 3.16
1.96 + 2.8x + x2 = 3.16

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = 3.16

Calculate the square root of the right side: 1.777638883

Break this problem into two subproblems by setting 
(x + 1.4) equal to 1.777638883 and -1.777638883.

Subproblem 1
x + 1.4 = 1.777638883

Simplifying
x + 1.4 = 1.777638883

Reorder the terms:
1.4 + x = 1.777638883

Solving
1.4 + x = 1.777638883

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 = 1.777638883 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = 1.777638883 + -1.4
x = 1.777638883 + -1.4

Combine like terms: 1.777638883 + -1.4 = 0.377638883
x = 0.377638883

Simplifying
x = 0.377638883

Subproblem 2
x + 1.4 = -1.777638883

Simplifying
x + 1.4 = -1.777638883

Reorder the terms:
1.4 + x = -1.777638883

Solving
1.4 + x = -1.777638883

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 = -1.777638883 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = -1.777638883 + -1.4
x = -1.777638883 + -1.4

Combine like terms: -1.777638883 + -1.4 = -3.177638883
x = -3.177638883

Simplifying
x = -3.177638883

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.377638883, -3.177638883}