(-4.9x^2)+20x+10=0

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Solution for (-4.9x^2)+20x+10=0 equation: 


Simplifying
(-4.9x2) + 20x + 10 = 0

Reorder the terms:
10 + 20x + (-4.9x2) = 0

Solving
10 + 20x + (-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'.
-2.040816327 + -4.081632653x + x2 = 0

Move the constant term to the right:

Add '2.040816327' to each side of the equation.
-2.040816327 + -4.081632653x + 2.040816327 + x2 = 0 + 2.040816327

Reorder the terms:
-2.040816327 + 2.040816327 + -4.081632653x + x2 = 0 + 2.040816327

Combine like terms: -2.040816327 + 2.040816327 = 0.000000000
0.000000000 + -4.081632653x + x2 = 0 + 2.040816327
-4.081632653x + x2 = 0 + 2.040816327

Combine like terms: 0 + 2.040816327 = 2.040816327
-4.081632653x + x2 = 2.040816327

The x term is -4.081632653x.  Take half its coefficient (-2.040816327).
Square it (4.164931281) and add it to both sides.

Add '4.164931281' to each side of the equation.
-4.081632653x + 4.164931281 + x2 = 2.040816327 + 4.164931281

Reorder the terms:
4.164931281 + -4.081632653x + x2 = 2.040816327 + 4.164931281

Combine like terms: 2.040816327 + 4.164931281 = 6.205747608
4.164931281 + -4.081632653x + x2 = 6.205747608

Factor a perfect square on the left side:
((x) + -2.040816327)((x) + -2.040816327) = 6.205747608

Calculate the square root of the right side: 2.4911338

Break this problem into two subproblems by setting 
((x) + -2.040816327) equal to 2.4911338 and -2.4911338.


Subproblem 1
(x) + -2.040816327 = 2.4911338

Simplifying
(x) + -2.040816327 = 2.4911338
x + -2.040816327 = 2.4911338

Reorder the terms:
-2.040816327 + x = 2.4911338

Solving
-2.040816327 + x = 2.4911338

Solving for variable 'x'.

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

Add '2.040816327' to each side of the equation.
-2.040816327 + 2.040816327 + x = 2.4911338 + 2.040816327

Combine like terms: -2.040816327 + 2.040816327 = 0.000000000
0.000000000 + x = 2.4911338 + 2.040816327
x = 2.4911338 + 2.040816327

Combine like terms: 2.4911338 + 2.040816327 = 4.531950127
x = 4.531950127

Simplifying
x = 4.531950127


Subproblem 2
(x) + -2.040816327 = -2.4911338

Simplifying
(x) + -2.040816327 = -2.4911338
x + -2.040816327 = -2.4911338

Reorder the terms:
-2.040816327 + x = -2.4911338

Solving
-2.040816327 + x = -2.4911338

Solving for variable 'x'.

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

Add '2.040816327' to each side of the equation.
-2.040816327 + 2.040816327 + x = -2.4911338 + 2.040816327

Combine like terms: -2.040816327 + 2.040816327 = 0.000000000
0.000000000 + x = -2.4911338 + 2.040816327
x = -2.4911338 + 2.040816327

Combine like terms: -2.4911338 + 2.040816327 = -0.450317473
x = -0.450317473

Simplifying
x = -0.450317473


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.531950127, -0.450317473}

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