.2121=14.37(x)+.5(-9.8)(x^2)

Solution for .2121=14.37(x)+.5(-9.8)(x^2) equation:

Simplifying
0.2121 = 14.37(x) + 0.5(-9.8)(x2)

Multiply 0.5 * -9.8
0.2121 = 14.37x + -4.9x2

Solving
0.2121 = 14.37x + -4.9x2

Solving for variable 'x'.

Reorder the terms:
0.2121 + -14.37x + 4.9x2 = 14.37x + -14.37x + -4.9x2 + 4.9x2

Combine like terms: 14.37x + -14.37x = 0.00
0.2121 + -14.37x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2
0.2121 + -14.37x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
0.2121 + -14.37x + 4.9x2 = 0.0

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

Divide each side by '4.9'.
0.04328571429 + -2.932653061x + x2 = 0

Move the constant term to the right:

Add '-0.04328571429' to each side of the equation.
0.04328571429 + -2.932653061x + -0.04328571429 + x2 = 0 + -0.04328571429

Reorder the terms:
0.04328571429 + -0.04328571429 + -2.932653061x + x2 = 0 + -0.04328571429

Combine like terms: 0.04328571429 + -0.04328571429 = 0.00000000000
0.00000000000 + -2.932653061x + x2 = 0 + -0.04328571429
-2.932653061x + x2 = 0 + -0.04328571429

Combine like terms: 0 + -0.04328571429 = -0.04328571429
-2.932653061x + x2 = -0.04328571429

The x term is -2.932653061x.  Take half its coefficient (-1.466326531).
Square it (2.150113496) and add it to both sides.

Add '2.150113496' to each side of the equation.
-2.932653061x + 2.150113496 + x2 = -0.04328571429 + 2.150113496

Reorder the terms:
2.150113496 + -2.932653061x + x2 = -0.04328571429 + 2.150113496

Combine like terms: -0.04328571429 + 2.150113496 = 2.10682778171
2.150113496 + -2.932653061x + x2 = 2.10682778171

Factor a perfect square on the left side:
(x + -1.466326531)(x + -1.466326531) = 2.10682778171

Calculate the square root of the right side: 1.451491571

Break this problem into two subproblems by setting 
(x + -1.466326531) equal to 1.451491571 and -1.451491571.

Subproblem 1
x + -1.466326531 = 1.451491571

Simplifying
x + -1.466326531 = 1.451491571

Reorder the terms:
-1.466326531 + x = 1.451491571

Solving
-1.466326531 + x = 1.451491571

Solving for variable 'x'.

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

Add '1.466326531' to each side of the equation.
-1.466326531 + 1.466326531 + x = 1.451491571 + 1.466326531

Combine like terms: -1.466326531 + 1.466326531 = 0.000000000
0.000000000 + x = 1.451491571 + 1.466326531
x = 1.451491571 + 1.466326531

Combine like terms: 1.451491571 + 1.466326531 = 2.917818102
x = 2.917818102

Simplifying
x = 2.917818102

Subproblem 2
x + -1.466326531 = -1.451491571

Simplifying
x + -1.466326531 = -1.451491571

Reorder the terms:
-1.466326531 + x = -1.451491571

Solving
-1.466326531 + x = -1.451491571

Solving for variable 'x'.

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

Add '1.466326531' to each side of the equation.
-1.466326531 + 1.466326531 + x = -1.451491571 + 1.466326531

Combine like terms: -1.466326531 + 1.466326531 = 0.000000000
0.000000000 + x = -1.451491571 + 1.466326531
x = -1.451491571 + 1.466326531

Combine like terms: -1.451491571 + 1.466326531 = 0.01483496
x = 0.01483496

Simplifying
x = 0.01483496

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.917818102, 0.01483496}