(-4.9x^2)+12.04x-3.05=0

Solution for (-4.9x^2)+12.04x-3.05=0 equation:

Simplifying
(-4.9x2) + 12.04x + -3.05 = 0

Reorder the terms:
-3.05 + 12.04x + (-4.9x2) = 0

Solving
-3.05 + 12.04x + (-4.9x2) = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
0.6224489796 + -2.457142857x + x2 = 0

Move the constant term to the right:

Add '-0.6224489796' to each side of the equation.
0.6224489796 + -2.457142857x + -0.6224489796 + x2 = 0 + -0.6224489796

Reorder the terms:
0.6224489796 + -0.6224489796 + -2.457142857x + x2 = 0 + -0.6224489796

Combine like terms: 0.6224489796 + -0.6224489796 = 0.0000000000
0.0000000000 + -2.457142857x + x2 = 0 + -0.6224489796
-2.457142857x + x2 = 0 + -0.6224489796

Combine like terms: 0 + -0.6224489796 = -0.6224489796
-2.457142857x + x2 = -0.6224489796

The x term is -2.457142857x.  Take half its coefficient (-1.228571429).
Square it (1.509387756) and add it to both sides.

Add '1.509387756' to each side of the equation.
-2.457142857x + 1.509387756 + x2 = -0.6224489796 + 1.509387756

Reorder the terms:
1.509387756 + -2.457142857x + x2 = -0.6224489796 + 1.509387756

Combine like terms: -0.6224489796 + 1.509387756 = 0.8869387764
1.509387756 + -2.457142857x + x2 = 0.8869387764

Factor a perfect square on the left side:
((x) + -1.228571429)((x) + -1.228571429) = 0.8869387764

Calculate the square root of the right side: 0.94177427

Break this problem into two subproblems by setting 
((x) + -1.228571429) equal to 0.94177427 and -0.94177427.

Subproblem 1
(x) + -1.228571429 = 0.94177427

Simplifying
(x) + -1.228571429 = 0.94177427
x + -1.228571429 = 0.94177427

Reorder the terms:
-1.228571429 + x = 0.94177427

Solving
-1.228571429 + x = 0.94177427

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.228571429' to each side of the equation.
-1.228571429 + 1.228571429 + x = 0.94177427 + 1.228571429

Combine like terms: -1.228571429 + 1.228571429 = 0.000000000
0.000000000 + x = 0.94177427 + 1.228571429
x = 0.94177427 + 1.228571429

Combine like terms: 0.94177427 + 1.228571429 = 2.170345699
x = 2.170345699

Simplifying
x = 2.170345699

Subproblem 2
(x) + -1.228571429 = -0.94177427

Simplifying
(x) + -1.228571429 = -0.94177427
x + -1.228571429 = -0.94177427

Reorder the terms:
-1.228571429 + x = -0.94177427

Solving
-1.228571429 + x = -0.94177427

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.228571429' to each side of the equation.
-1.228571429 + 1.228571429 + x = -0.94177427 + 1.228571429

Combine like terms: -1.228571429 + 1.228571429 = 0.000000000
0.000000000 + x = -0.94177427 + 1.228571429
x = -0.94177427 + 1.228571429

Combine like terms: -0.94177427 + 1.228571429 = 0.286797159
x = 0.286797159

Simplifying
x = 0.286797159

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.170345699, 0.286797159}