0=5x^2+10x-3

Solution for 0=5x^2+10x-3 equation:

Simplifying
0 = 5x2 + 10x + -3

Reorder the terms:
0 = -3 + 10x + 5x2

Solving
0 = -3 + 10x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -10x + -5x2 = -3 + 10x + 5x2 + 3 + -10x + -5x2

Reorder the terms:
3 + -10x + -5x2 = -3 + 3 + 10x + -10x + 5x2 + -5x2

Combine like terms: -3 + 3 = 0
3 + -10x + -5x2 = 0 + 10x + -10x + 5x2 + -5x2
3 + -10x + -5x2 = 10x + -10x + 5x2 + -5x2

Combine like terms: 10x + -10x = 0
3 + -10x + -5x2 = 0 + 5x2 + -5x2
3 + -10x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
3 + -10x + -5x2 = 0

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

Divide each side by '-5'.
-0.6 + 2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 2x + x2 = 0 + 0.6
2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
2x + x2 = 0.6

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.6 + 1

Reorder the terms:
1 + 2x + x2 = 0.6 + 1

Combine like terms: 0.6 + 1 = 1.6
1 + 2x + x2 = 1.6

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.6

Calculate the square root of the right side: 1.264911064

Break this problem into two subproblems by setting 
(x + 1) equal to 1.264911064 and -1.264911064.

Subproblem 1
x + 1 = 1.264911064

Simplifying
x + 1 = 1.264911064

Reorder the terms:
1 + x = 1.264911064

Solving
1 + x = 1.264911064

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.264911064 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.264911064 + -1
x = 1.264911064 + -1

Combine like terms: 1.264911064 + -1 = 0.264911064
x = 0.264911064

Simplifying
x = 0.264911064

Subproblem 2
x + 1 = -1.264911064

Simplifying
x + 1 = -1.264911064

Reorder the terms:
1 + x = -1.264911064

Solving
1 + x = -1.264911064

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.264911064 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.264911064 + -1
x = -1.264911064 + -1

Combine like terms: -1.264911064 + -1 = -2.264911064
x = -2.264911064

Simplifying
x = -2.264911064

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.264911064, -2.264911064}