-5x^2+16x-6=3

Solution for -5x^2+16x-6=3 equation:

Simplifying
-5x2 + 16x + -6 = 3

Reorder the terms:
-6 + 16x + -5x2 = 3

Solving
-6 + 16x + -5x2 = 3

Solving for variable 'x'.

Reorder the terms:
-6 + -3 + 16x + -5x2 = 3 + -3

Combine like terms: -6 + -3 = -9
-9 + 16x + -5x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-9 + 16x + -5x2 = 0

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

Divide each side by '-5'.
1.8 + -3.2x + x2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + -3.2x + -1.8 + x2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + -3.2x + x2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + -3.2x + x2 = 0 + -1.8
-3.2x + x2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
-3.2x + x2 = -1.8

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = -1.8 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = -1.8 + 2.56

Combine like terms: -1.8 + 2.56 = 0.76
2.56 + -3.2x + x2 = 0.76

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 0.76

Calculate the square root of the right side: 0.871779789

Break this problem into two subproblems by setting 
(x + -1.6) equal to 0.871779789 and -0.871779789.

Subproblem 1
x + -1.6 = 0.871779789

Simplifying
x + -1.6 = 0.871779789

Reorder the terms:
-1.6 + x = 0.871779789

Solving
-1.6 + x = 0.871779789

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = 0.871779789 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = 0.871779789 + 1.6
x = 0.871779789 + 1.6

Combine like terms: 0.871779789 + 1.6 = 2.471779789
x = 2.471779789

Simplifying
x = 2.471779789

Subproblem 2
x + -1.6 = -0.871779789

Simplifying
x + -1.6 = -0.871779789

Reorder the terms:
-1.6 + x = -0.871779789

Solving
-1.6 + x = -0.871779789

Solving for variable 'x'.

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

Add '1.6' to each side of the equation.
-1.6 + 1.6 + x = -0.871779789 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + x = -0.871779789 + 1.6
x = -0.871779789 + 1.6

Combine like terms: -0.871779789 + 1.6 = 0.728220211
x = 0.728220211

Simplifying
x = 0.728220211

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.471779789, 0.728220211}