0.75x^2+1.23x-2.48=0

Solution for 0.75x^2+1.23x-2.48=0 equation:

Simplifying
0.75x2 + 1.23x + -2.48 = 0

Reorder the terms:
-2.48 + 1.23x + 0.75x2 = 0

Solving
-2.48 + 1.23x + 0.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.75'.
-3.306666667 + 1.64x + x2 = 0

Move the constant term to the right:

Add '3.306666667' to each side of the equation.
-3.306666667 + 1.64x + 3.306666667 + x2 = 0 + 3.306666667

Reorder the terms:
-3.306666667 + 3.306666667 + 1.64x + x2 = 0 + 3.306666667

Combine like terms: -3.306666667 + 3.306666667 = 0.000000000
0.000000000 + 1.64x + x2 = 0 + 3.306666667
1.64x + x2 = 0 + 3.306666667

Combine like terms: 0 + 3.306666667 = 3.306666667
1.64x + x2 = 3.306666667

The x term is 1.64x.  Take half its coefficient (0.82).
Square it (0.6724) and add it to both sides.

Add '0.6724' to each side of the equation.
1.64x + 0.6724 + x2 = 3.306666667 + 0.6724

Reorder the terms:
0.6724 + 1.64x + x2 = 3.306666667 + 0.6724

Combine like terms: 3.306666667 + 0.6724 = 3.979066667
0.6724 + 1.64x + x2 = 3.979066667

Factor a perfect square on the left side:
(x + 0.82)(x + 0.82) = 3.979066667

Calculate the square root of the right side: 1.994759802

Break this problem into two subproblems by setting 
(x + 0.82) equal to 1.994759802 and -1.994759802.

Subproblem 1
x + 0.82 = 1.994759802

Simplifying
x + 0.82 = 1.994759802

Reorder the terms:
0.82 + x = 1.994759802

Solving
0.82 + x = 1.994759802

Solving for variable 'x'.

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

Add '-0.82' to each side of the equation.
0.82 + -0.82 + x = 1.994759802 + -0.82

Combine like terms: 0.82 + -0.82 = 0.00
0.00 + x = 1.994759802 + -0.82
x = 1.994759802 + -0.82

Combine like terms: 1.994759802 + -0.82 = 1.174759802
x = 1.174759802

Simplifying
x = 1.174759802

Subproblem 2
x + 0.82 = -1.994759802

Simplifying
x + 0.82 = -1.994759802

Reorder the terms:
0.82 + x = -1.994759802

Solving
0.82 + x = -1.994759802

Solving for variable 'x'.

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

Add '-0.82' to each side of the equation.
0.82 + -0.82 + x = -1.994759802 + -0.82

Combine like terms: 0.82 + -0.82 = 0.00
0.00 + x = -1.994759802 + -0.82
x = -1.994759802 + -0.82

Combine like terms: -1.994759802 + -0.82 = -2.814759802
x = -2.814759802

Simplifying
x = -2.814759802

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.174759802, -2.814759802}