4x^2=-6+8x

Solution for 4x^2=-6+8x equation:

Simplifying
4x2 = -6 + 8x

Solving
4x2 = -6 + 8x

Solving for variable 'x'.

Reorder the terms:
6 + -8x + 4x2 = -6 + 8x + 6 + -8x

Reorder the terms:
6 + -8x + 4x2 = -6 + 6 + 8x + -8x

Combine like terms: -6 + 6 = 0
6 + -8x + 4x2 = 0 + 8x + -8x
6 + -8x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
6 + -8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -4x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + -4x + 2x2 = 0

Solving
3 + -4x + 2x2 = 0

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

Divide each side by '2'.
1.5 + -2x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -2x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -2x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -2x + x2 = 0 + -1.5
-2x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-2x + x2 = -1.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -1.5 + 1

Reorder the terms:
1 + -2x + x2 = -1.5 + 1

Combine like terms: -1.5 + 1 = -0.5
1 + -2x + x2 = -0.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = -0.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.