x(x+5)=4x^2+6

Solution for x(x+5)=4x^2+6 equation:

Simplifying
x(x + 5) = 4x2 + 6

Reorder the terms:
x(5 + x) = 4x2 + 6
(5 * x + x * x) = 4x2 + 6
(5x + x2) = 4x2 + 6

Reorder the terms:
5x + x2 = 6 + 4x2

Solving
5x + x2 = 6 + 4x2

Solving for variable 'x'.

Reorder the terms:
-6 + 5x + x2 + -4x2 = 6 + 4x2 + -6 + -4x2

Combine like terms: x2 + -4x2 = -3x2
-6 + 5x + -3x2 = 6 + 4x2 + -6 + -4x2

Reorder the terms:
-6 + 5x + -3x2 = 6 + -6 + 4x2 + -4x2

Combine like terms: 6 + -6 = 0
-6 + 5x + -3x2 = 0 + 4x2 + -4x2
-6 + 5x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-6 + 5x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
2 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1.666666667x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -1.666666667x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1.666666667x + x2 = 0 + -2
-1.666666667x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1.666666667x + x2 = -2

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -2 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -2 + 0.6944444447

Combine like terms: -2 + 0.6944444447 = -1.3055555553
0.6944444447 + -1.666666667x + x2 = -1.3055555553

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = -1.3055555553

Can't calculate square root of the right side.

The solution to this equation could not be determined.