x(2x+4.5)=2(2x-1)+4x

Solution for x(2x+4.5)=2(2x-1)+4x equation:

Simplifying
x(2x + 4.5) = 2(2x + -1) + 4x

Reorder the terms:
x(4.5 + 2x) = 2(2x + -1) + 4x
(4.5 * x + 2x * x) = 2(2x + -1) + 4x
(4.5x + 2x2) = 2(2x + -1) + 4x

Reorder the terms:
4.5x + 2x2 = 2(-1 + 2x) + 4x
4.5x + 2x2 = (-1 * 2 + 2x * 2) + 4x
4.5x + 2x2 = (-2 + 4x) + 4x

Combine like terms: 4x + 4x = 8x
4.5x + 2x2 = -2 + 8x

Solving
4.5x + 2x2 = -2 + 8x

Solving for variable 'x'.

Reorder the terms:
2 + 4.5x + -8x + 2x2 = -2 + 8x + 2 + -8x

Combine like terms: 4.5x + -8x = -3.5x
2 + -3.5x + 2x2 = -2 + 8x + 2 + -8x

Reorder the terms:
2 + -3.5x + 2x2 = -2 + 2 + 8x + -8x

Combine like terms: -2 + 2 = 0
2 + -3.5x + 2x2 = 0 + 8x + -8x
2 + -3.5x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
2 + -3.5x + 2x2 = 0

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

Divide each side by '2'.
1 + -1.75x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.75x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.75x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.75x + x2 = 0 + -1
-1.75x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.75x + x2 = -1

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = -1 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = -1 + 0.765625

Combine like terms: -1 + 0.765625 = -0.234375
0.765625 + -1.75x + x2 = -0.234375

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = -0.234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.