1.829=-4.9x^2+4.9x+0.8

Solution for 1.829=-4.9x^2+4.9x+0.8 equation:

Simplifying
1.829 = -4.9x2 + 4.9x + 0.8

Reorder the terms:
1.829 = 0.8 + 4.9x + -4.9x2

Solving
1.829 = 0.8 + 4.9x + -4.9x2

Solving for variable 'x'.

Combine like terms: 1.829 + -0.8 = 1.029
1.029 + -4.9x + 4.9x2 = 0.8 + 4.9x + -4.9x2 + -0.8 + -4.9x + 4.9x2

Reorder the terms:
1.029 + -4.9x + 4.9x2 = 0.8 + -0.8 + 4.9x + -4.9x + -4.9x2 + 4.9x2

Combine like terms: 0.8 + -0.8 = 0.0
1.029 + -4.9x + 4.9x2 = 0.0 + 4.9x + -4.9x + -4.9x2 + 4.9x2
1.029 + -4.9x + 4.9x2 = 4.9x + -4.9x + -4.9x2 + 4.9x2

Combine like terms: 4.9x + -4.9x = 0.0
1.029 + -4.9x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2
1.029 + -4.9x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
1.029 + -4.9x + 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'.
0.21 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.21' to each side of the equation.
0.21 + -1x + -0.21 + x2 = 0 + -0.21

Reorder the terms:
0.21 + -0.21 + -1x + x2 = 0 + -0.21

Combine like terms: 0.21 + -0.21 = 0.00
0.00 + -1x + x2 = 0 + -0.21
-1x + x2 = 0 + -0.21

Combine like terms: 0 + -0.21 = -0.21
-1x + x2 = -0.21

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.21 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.21 + 0.25

Combine like terms: -0.21 + 0.25 = 0.04
0.25 + -1x + x2 = 0.04

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.04

Calculate the square root of the right side: 0.2

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.2 and -0.2.

Subproblem 1
x + -0.5 = 0.2

Simplifying
x + -0.5 = 0.2

Reorder the terms:
-0.5 + x = 0.2

Solving
-0.5 + x = 0.2

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.2 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.2 + 0.5
x = 0.2 + 0.5

Combine like terms: 0.2 + 0.5 = 0.7
x = 0.7

Simplifying
x = 0.7

Subproblem 2
x + -0.5 = -0.2

Simplifying
x + -0.5 = -0.2

Reorder the terms:
-0.5 + x = -0.2

Solving
-0.5 + x = -0.2

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.2 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.2 + 0.5
x = -0.2 + 0.5

Combine like terms: -0.2 + 0.5 = 0.3
x = 0.3

Simplifying
x = 0.3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7, 0.3}