5x^2=10x-3

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

Simplifying
5x2 = 10x + -3

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

Solving
5x2 = -3 + 10x

Solving for variable 'x'.

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

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

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

Combine like terms: 10x + -10x = 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 = 0.4
1 + -2x + x2 = 0.4

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(x + -1) equal to 0.632455532 and -0.632455532.

Subproblem 1
x + -1 = 0.632455532

Simplifying
x + -1 = 0.632455532

Reorder the terms:
-1 + x = 0.632455532

Solving
-1 + x = 0.632455532

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 = 0.632455532 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0.632455532 + 1
x = 0.632455532 + 1

Combine like terms: 0.632455532 + 1 = 1.632455532
x = 1.632455532

Simplifying
x = 1.632455532

Subproblem 2
x + -1 = -0.632455532

Simplifying
x + -1 = -0.632455532

Reorder the terms:
-1 + x = -0.632455532

Solving
-1 + x = -0.632455532

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 = -0.632455532 + 1

Combine like terms: -1 + 1 = 0
0 + x = -0.632455532 + 1
x = -0.632455532 + 1

Combine like terms: -0.632455532 + 1 = 0.367544468
x = 0.367544468

Simplifying
x = 0.367544468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.632455532, 0.367544468}