x(x+1)=6x^2+4

Solution for x(x+1)=6x^2+4 equation:

Simplifying
x(x + 1) = 6x2 + 4

Reorder the terms:
x(1 + x) = 6x2 + 4
(1 * x + x * x) = 6x2 + 4
(1x + x2) = 6x2 + 4

Reorder the terms:
1x + x2 = 4 + 6x2

Solving
1x + x2 = 4 + 6x2

Solving for variable 'x'.

Reorder the terms:
-4 + 1x + x2 + -6x2 = 4 + 6x2 + -4 + -6x2

Combine like terms: x2 + -6x2 = -5x2
-4 + 1x + -5x2 = 4 + 6x2 + -4 + -6x2

Reorder the terms:
-4 + 1x + -5x2 = 4 + -4 + 6x2 + -6x2

Combine like terms: 4 + -4 = 0
-4 + 1x + -5x2 = 0 + 6x2 + -6x2
-4 + 1x + -5x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-4 + 1x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.8 + -0.2x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -0.2x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -0.2x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -0.2x + x2 = 0 + -0.8
-0.2x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-0.2x + x2 = -0.8

The x term is -0.2x.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x + 0.01 + x2 = -0.8 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = -0.8 + 0.01

Combine like terms: -0.8 + 0.01 = -0.79
0.01 + -0.2x + x2 = -0.79

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = -0.79

Can't calculate square root of the right side.

The solution to this equation could not be determined.