20x^2-47x+4=0

Solution for 20x^2-47x+4=0 equation:

Simplifying
20x2 + -47x + 4 = 0

Reorder the terms:
4 + -47x + 20x2 = 0

Solving
4 + -47x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
0.2 + -2.35x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -2.35x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -2.35x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -2.35x + x2 = 0 + -0.2
-2.35x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-2.35x + x2 = -0.2

The x term is -2.35x.  Take half its coefficient (-1.175).
Square it (1.380625) and add it to both sides.

Add '1.380625' to each side of the equation.
-2.35x + 1.380625 + x2 = -0.2 + 1.380625

Reorder the terms:
1.380625 + -2.35x + x2 = -0.2 + 1.380625

Combine like terms: -0.2 + 1.380625 = 1.180625
1.380625 + -2.35x + x2 = 1.180625

Factor a perfect square on the left side:
(x + -1.175)(x + -1.175) = 1.180625

Calculate the square root of the right side: 1.086565691

Break this problem into two subproblems by setting 
(x + -1.175) equal to 1.086565691 and -1.086565691.

Subproblem 1
x + -1.175 = 1.086565691

Simplifying
x + -1.175 = 1.086565691

Reorder the terms:
-1.175 + x = 1.086565691

Solving
-1.175 + x = 1.086565691

Solving for variable 'x'.

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

Add '1.175' to each side of the equation.
-1.175 + 1.175 + x = 1.086565691 + 1.175

Combine like terms: -1.175 + 1.175 = 0.000
0.000 + x = 1.086565691 + 1.175
x = 1.086565691 + 1.175

Combine like terms: 1.086565691 + 1.175 = 2.261565691
x = 2.261565691

Simplifying
x = 2.261565691

Subproblem 2
x + -1.175 = -1.086565691

Simplifying
x + -1.175 = -1.086565691

Reorder the terms:
-1.175 + x = -1.086565691

Solving
-1.175 + x = -1.086565691

Solving for variable 'x'.

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

Add '1.175' to each side of the equation.
-1.175 + 1.175 + x = -1.086565691 + 1.175

Combine like terms: -1.175 + 1.175 = 0.000
0.000 + x = -1.086565691 + 1.175
x = -1.086565691 + 1.175

Combine like terms: -1.086565691 + 1.175 = 0.088434309
x = 0.088434309

Simplifying
x = 0.088434309

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.261565691, 0.088434309}