x^2+4.8x-3=0

Solution for x^2+4.8x-3=0 equation:

Simplifying
x2 + 4.8x + -3 = 0

Reorder the terms:
-3 + 4.8x + x2 = 0

Solving
-3 + 4.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 4.8x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 4.8x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4.8x + x2 = 0 + 3
4.8x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
4.8x + x2 = 3

The x term is 4.8x.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8x + 5.76 + x2 = 3 + 5.76

Reorder the terms:
5.76 + 4.8x + x2 = 3 + 5.76

Combine like terms: 3 + 5.76 = 8.76
5.76 + 4.8x + x2 = 8.76

Factor a perfect square on the left side:
(x + 2.4)(x + 2.4) = 8.76

Calculate the square root of the right side: 2.959729717

Break this problem into two subproblems by setting 
(x + 2.4) equal to 2.959729717 and -2.959729717.

Subproblem 1
x + 2.4 = 2.959729717

Simplifying
x + 2.4 = 2.959729717

Reorder the terms:
2.4 + x = 2.959729717

Solving
2.4 + x = 2.959729717

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = 2.959729717 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = 2.959729717 + -2.4
x = 2.959729717 + -2.4

Combine like terms: 2.959729717 + -2.4 = 0.559729717
x = 0.559729717

Simplifying
x = 0.559729717

Subproblem 2
x + 2.4 = -2.959729717

Simplifying
x + 2.4 = -2.959729717

Reorder the terms:
2.4 + x = -2.959729717

Solving
2.4 + x = -2.959729717

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = -2.959729717 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = -2.959729717 + -2.4
x = -2.959729717 + -2.4

Combine like terms: -2.959729717 + -2.4 = -5.359729717
x = -5.359729717

Simplifying
x = -5.359729717

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.559729717, -5.359729717}