x(x+6)=9x^2+3

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Solution for x(x+6)=9x^2+3 equation: 


Simplifying
x(x + 6) = 9x2 + 3

Reorder the terms:
x(6 + x) = 9x2 + 3
(6 * x + x * x) = 9x2 + 3
(6x + x2) = 9x2 + 3

Reorder the terms:
6x + x2 = 3 + 9x2

Solving
6x + x2 = 3 + 9x2

Solving for variable 'x'.

Reorder the terms:
-3 + 6x + x2 + -9x2 = 3 + 9x2 + -3 + -9x2

Combine like terms: x2 + -9x2 = -8x2
-3 + 6x + -8x2 = 3 + 9x2 + -3 + -9x2

Reorder the terms:
-3 + 6x + -8x2 = 3 + -3 + 9x2 + -9x2

Combine like terms: 3 + -3 = 0
-3 + 6x + -8x2 = 0 + 9x2 + -9x2
-3 + 6x + -8x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-3 + 6x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.375 + -0.75x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -0.75x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -0.75x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -0.75x + x2 = 0 + -0.375
-0.75x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-0.75x + x2 = -0.375

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = -0.375 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = -0.375 + 0.140625

Combine like terms: -0.375 + 0.140625 = -0.234375
0.140625 + -0.75x + x2 = -0.234375

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = -0.234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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