5x^2=3-8x

Solution for 5x^2=3-8x equation:

Simplifying
5x2 = 3 + -8x

Solving
5x2 = 3 + -8x

Solving for variable 'x'.

Reorder the terms:
-3 + 8x + 5x2 = 3 + -8x + -3 + 8x

Reorder the terms:
-3 + 8x + 5x2 = 3 + -3 + -8x + 8x

Combine like terms: 3 + -3 = 0
-3 + 8x + 5x2 = 0 + -8x + 8x
-3 + 8x + 5x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-3 + 8x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + 1.6x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 1.6x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 1.6x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 1.6x + x2 = 0 + 0.6
1.6x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
1.6x + x2 = 0.6

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 0.6 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 0.6 + 0.64

Combine like terms: 0.6 + 0.64 = 1.24
0.64 + 1.6x + x2 = 1.24

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(x + 0.8) equal to 1.113552873 and -1.113552873.

Subproblem 1
x + 0.8 = 1.113552873

Simplifying
x + 0.8 = 1.113552873

Reorder the terms:
0.8 + x = 1.113552873

Solving
0.8 + x = 1.113552873

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 1.113552873 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 1.113552873 + -0.8
x = 1.113552873 + -0.8

Combine like terms: 1.113552873 + -0.8 = 0.313552873
x = 0.313552873

Simplifying
x = 0.313552873

Subproblem 2
x + 0.8 = -1.113552873

Simplifying
x + 0.8 = -1.113552873

Reorder the terms:
0.8 + x = -1.113552873

Solving
0.8 + x = -1.113552873

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -1.113552873 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -1.113552873 + -0.8
x = -1.113552873 + -0.8

Combine like terms: -1.113552873 + -0.8 = -1.913552873
x = -1.913552873

Simplifying
x = -1.913552873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.313552873, -1.913552873}