0=5x^2+20x-3

Solution for 0=5x^2+20x-3 equation:

Simplifying
0 = 5x2 + 20x + -3

Reorder the terms:
0 = -3 + 20x + 5x2

Solving
0 = -3 + 20x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -20x + -5x2 = -3 + 20x + 5x2 + 3 + -20x + -5x2

Reorder the terms:
3 + -20x + -5x2 = -3 + 3 + 20x + -20x + 5x2 + -5x2

Combine like terms: -3 + 3 = 0
3 + -20x + -5x2 = 0 + 20x + -20x + 5x2 + -5x2
3 + -20x + -5x2 = 20x + -20x + 5x2 + -5x2

Combine like terms: 20x + -20x = 0
3 + -20x + -5x2 = 0 + 5x2 + -5x2
3 + -20x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
3 + -20x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.6 + 4x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 4x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 4x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 4x + x2 = 0 + 0.6
4x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
4x + x2 = 0.6

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 0.6 + 4

Reorder the terms:
4 + 4x + x2 = 0.6 + 4

Combine like terms: 0.6 + 4 = 4.6
4 + 4x + x2 = 4.6

Factor a perfect square on the left side:
(x + 2)(x + 2) = 4.6

Calculate the square root of the right side: 2.144761059

Break this problem into two subproblems by setting 
(x + 2) equal to 2.144761059 and -2.144761059.

Subproblem 1
x + 2 = 2.144761059

Simplifying
x + 2 = 2.144761059

Reorder the terms:
2 + x = 2.144761059

Solving
2 + x = 2.144761059

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.144761059 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.144761059 + -2
x = 2.144761059 + -2

Combine like terms: 2.144761059 + -2 = 0.144761059
x = 0.144761059

Simplifying
x = 0.144761059

Subproblem 2
x + 2 = -2.144761059

Simplifying
x + 2 = -2.144761059

Reorder the terms:
2 + x = -2.144761059

Solving
2 + x = -2.144761059

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.144761059 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.144761059 + -2
x = -2.144761059 + -2

Combine like terms: -2.144761059 + -2 = -4.144761059
x = -4.144761059

Simplifying
x = -4.144761059

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.144761059, -4.144761059}