(4x^2-6)=(-2x^2+19x)

Solution for (4x^2-6)=(-2x^2+19x) equation:

Simplifying
(4x2 + -6) = (-2x2 + 19x)

Reorder the terms:
(-6 + 4x2) = (-2x2 + 19x)

Remove parenthesis around (-6 + 4x2)
-6 + 4x2 = (-2x2 + 19x)

Reorder the terms:
-6 + 4x2 = (19x + -2x2)

Remove parenthesis around (19x + -2x2)
-6 + 4x2 = 19x + -2x2

Solving
-6 + 4x2 = 19x + -2x2

Solving for variable 'x'.

Reorder the terms:
-6 + -19x + 4x2 + 2x2 = 19x + -2x2 + -19x + 2x2

Combine like terms: 4x2 + 2x2 = 6x2
-6 + -19x + 6x2 = 19x + -2x2 + -19x + 2x2

Reorder the terms:
-6 + -19x + 6x2 = 19x + -19x + -2x2 + 2x2

Combine like terms: 19x + -19x = 0
-6 + -19x + 6x2 = 0 + -2x2 + 2x2
-6 + -19x + 6x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-6 + -19x + 6x2 = 0

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

Divide each side by '6'.
-1 + -3.166666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3.166666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3.166666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3.166666667x + x2 = 0 + 1
-3.166666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3.166666667x + x2 = 1

The x term is -3.166666667x.  Take half its coefficient (-1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
-3.166666667x + 2.506944447 + x2 = 1 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667x + x2 = 1 + 2.506944447

Combine like terms: 1 + 2.506944447 = 3.506944447
2.506944447 + -3.166666667x + x2 = 3.506944447

Factor a perfect square on the left side:
(x + -1.583333334)(x + -1.583333334) = 3.506944447

Calculate the square root of the right side: 1.872683755

Break this problem into two subproblems by setting 
(x + -1.583333334) equal to 1.872683755 and -1.872683755.

Subproblem 1
x + -1.583333334 = 1.872683755

Simplifying
x + -1.583333334 = 1.872683755

Reorder the terms:
-1.583333334 + x = 1.872683755

Solving
-1.583333334 + x = 1.872683755

Solving for variable 'x'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + x = 1.872683755 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = 1.872683755 + 1.583333334
x = 1.872683755 + 1.583333334

Combine like terms: 1.872683755 + 1.583333334 = 3.456017089
x = 3.456017089

Simplifying
x = 3.456017089

Subproblem 2
x + -1.583333334 = -1.872683755

Simplifying
x + -1.583333334 = -1.872683755

Reorder the terms:
-1.583333334 + x = -1.872683755

Solving
-1.583333334 + x = -1.872683755

Solving for variable 'x'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + x = -1.872683755 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = -1.872683755 + 1.583333334
x = -1.872683755 + 1.583333334

Combine like terms: -1.872683755 + 1.583333334 = -0.289350421
x = -0.289350421

Simplifying
x = -0.289350421

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.456017089, -0.289350421}