5x^2+22x-3=0

Solution for 5x^2+22x-3=0 equation:

Simplifying
5x2 + 22x + -3 = 0

Reorder the terms:
-3 + 22x + 5x2 = 0

Solving
-3 + 22x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.6 + 4.4x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 4.4x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 4.4x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 4.4x + x2 = 0 + 0.6
4.4x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
4.4x + x2 = 0.6

The x term is 4.4x.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4x + 4.84 + x2 = 0.6 + 4.84

Reorder the terms:
4.84 + 4.4x + x2 = 0.6 + 4.84

Combine like terms: 0.6 + 4.84 = 5.44
4.84 + 4.4x + x2 = 5.44

Factor a perfect square on the left side:
(x + 2.2)(x + 2.2) = 5.44

Calculate the square root of the right side: 2.332380758

Break this problem into two subproblems by setting 
(x + 2.2) equal to 2.332380758 and -2.332380758.

Subproblem 1
x + 2.2 = 2.332380758

Simplifying
x + 2.2 = 2.332380758

Reorder the terms:
2.2 + x = 2.332380758

Solving
2.2 + x = 2.332380758

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = 2.332380758 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = 2.332380758 + -2.2
x = 2.332380758 + -2.2

Combine like terms: 2.332380758 + -2.2 = 0.132380758
x = 0.132380758

Simplifying
x = 0.132380758

Subproblem 2
x + 2.2 = -2.332380758

Simplifying
x + 2.2 = -2.332380758

Reorder the terms:
2.2 + x = -2.332380758

Solving
2.2 + x = -2.332380758

Solving for variable 'x'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + x = -2.332380758 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + x = -2.332380758 + -2.2
x = -2.332380758 + -2.2

Combine like terms: -2.332380758 + -2.2 = -4.532380758
x = -4.532380758

Simplifying
x = -4.532380758

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.132380758, -4.532380758}