0=-4.9(x^2)+21(x)+5

Solution for 0=-4.9(x^2)+21(x)+5 equation:

Simplifying
0 = -4.9(x2) + 21(x) + 5

Reorder the terms:
0 = 5 + 21x + -4.9x2

Solving
0 = 5 + 21x + -4.9x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -21x + 4.9x2 = 5 + 21x + -4.9x2 + -5 + -21x + 4.9x2

Reorder the terms:
-5 + -21x + 4.9x2 = 5 + -5 + 21x + -21x + -4.9x2 + 4.9x2

Combine like terms: 5 + -5 = 0
-5 + -21x + 4.9x2 = 0 + 21x + -21x + -4.9x2 + 4.9x2
-5 + -21x + 4.9x2 = 21x + -21x + -4.9x2 + 4.9x2

Combine like terms: 21x + -21x = 0
-5 + -21x + 4.9x2 = 0 + -4.9x2 + 4.9x2
-5 + -21x + 4.9x2 = -4.9x2 + 4.9x2

Combine like terms: -4.9x2 + 4.9x2 = 0.0
-5 + -21x + 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'.
-1.020408163 + -4.285714286x + x2 = 0

Move the constant term to the right:

Add '1.020408163' to each side of the equation.
-1.020408163 + -4.285714286x + 1.020408163 + x2 = 0 + 1.020408163

Reorder the terms:
-1.020408163 + 1.020408163 + -4.285714286x + x2 = 0 + 1.020408163

Combine like terms: -1.020408163 + 1.020408163 = 0.000000000
0.000000000 + -4.285714286x + x2 = 0 + 1.020408163
-4.285714286x + x2 = 0 + 1.020408163

Combine like terms: 0 + 1.020408163 = 1.020408163
-4.285714286x + x2 = 1.020408163

The x term is -4.285714286x.  Take half its coefficient (-2.142857143).
Square it (4.591836735) and add it to both sides.

Add '4.591836735' to each side of the equation.
-4.285714286x + 4.591836735 + x2 = 1.020408163 + 4.591836735

Reorder the terms:
4.591836735 + -4.285714286x + x2 = 1.020408163 + 4.591836735

Combine like terms: 1.020408163 + 4.591836735 = 5.612244898
4.591836735 + -4.285714286x + x2 = 5.612244898

Factor a perfect square on the left side:
(x + -2.142857143)(x + -2.142857143) = 5.612244898

Calculate the square root of the right side: 2.369017707

Break this problem into two subproblems by setting 
(x + -2.142857143) equal to 2.369017707 and -2.369017707.

Subproblem 1
x + -2.142857143 = 2.369017707

Simplifying
x + -2.142857143 = 2.369017707

Reorder the terms:
-2.142857143 + x = 2.369017707

Solving
-2.142857143 + x = 2.369017707

Solving for variable 'x'.

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

Add '2.142857143' to each side of the equation.
-2.142857143 + 2.142857143 + x = 2.369017707 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + x = 2.369017707 + 2.142857143
x = 2.369017707 + 2.142857143

Combine like terms: 2.369017707 + 2.142857143 = 4.51187485
x = 4.51187485

Simplifying
x = 4.51187485

Subproblem 2
x + -2.142857143 = -2.369017707

Simplifying
x + -2.142857143 = -2.369017707

Reorder the terms:
-2.142857143 + x = -2.369017707

Solving
-2.142857143 + x = -2.369017707

Solving for variable 'x'.

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

Add '2.142857143' to each side of the equation.
-2.142857143 + 2.142857143 + x = -2.369017707 + 2.142857143

Combine like terms: -2.142857143 + 2.142857143 = 0.000000000
0.000000000 + x = -2.369017707 + 2.142857143
x = -2.369017707 + 2.142857143

Combine like terms: -2.369017707 + 2.142857143 = -0.226160564
x = -0.226160564

Simplifying
x = -0.226160564

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.51187485, -0.226160564}