2x^2-5x-3=3

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

Simplifying
2x2 + -5x + -3 = 3

Reorder the terms:
-3 + -5x + 2x2 = 3

Solving
-3 + -5x + 2x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -3 + -5x + 2x2 = 3 + -3

Combine like terms: -3 + -3 = -6
-6 + -5x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + -5x + 2x2 = 0

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

Divide each side by '2'.
-3 + -2.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -2.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -2.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2.5x + x2 = 0 + 3
-2.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2.5x + x2 = 3

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 3 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + -2.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
x + -1.25 = 2.136000936

Simplifying
x + -1.25 = 2.136000936

Reorder the terms:
-1.25 + x = 2.136000936

Solving
-1.25 + x = 2.136000936

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 2.136000936 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.136000936 + 1.25
x = 2.136000936 + 1.25

Combine like terms: 2.136000936 + 1.25 = 3.386000936
x = 3.386000936

Simplifying
x = 3.386000936

Subproblem 2
x + -1.25 = -2.136000936

Simplifying
x + -1.25 = -2.136000936

Reorder the terms:
-1.25 + x = -2.136000936

Solving
-1.25 + x = -2.136000936

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -2.136000936 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.136000936 + 1.25
x = -2.136000936 + 1.25

Combine like terms: -2.136000936 + 1.25 = -0.886000936
x = -0.886000936

Simplifying
x = -0.886000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.386000936, -0.886000936}