324.2-58.5x-1.25x^2=0

Solution for 324.2-58.5x-1.25x^2=0 equation:

Simplifying
324.2 + -58.5x + -1.25x2 = 0

Solving
324.2 + -58.5x + -1.25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.25 the coefficient of the squared term: 

Divide each side by '-1.25'.
-259.36 + 46.8x + x2 = 0

Move the constant term to the right:

Add '259.36' to each side of the equation.
-259.36 + 46.8x + 259.36 + x2 = 0 + 259.36

Reorder the terms:
-259.36 + 259.36 + 46.8x + x2 = 0 + 259.36

Combine like terms: -259.36 + 259.36 = 0.00
0.00 + 46.8x + x2 = 0 + 259.36
46.8x + x2 = 0 + 259.36

Combine like terms: 0 + 259.36 = 259.36
46.8x + x2 = 259.36

The x term is 46.8x.  Take half its coefficient (23.4).
Square it (547.56) and add it to both sides.

Add '547.56' to each side of the equation.
46.8x + 547.56 + x2 = 259.36 + 547.56

Reorder the terms:
547.56 + 46.8x + x2 = 259.36 + 547.56

Combine like terms: 259.36 + 547.56 = 806.92
547.56 + 46.8x + x2 = 806.92

Factor a perfect square on the left side:
(x + 23.4)(x + 23.4) = 806.92

Calculate the square root of the right side: 28.406337321

Break this problem into two subproblems by setting 
(x + 23.4) equal to 28.406337321 and -28.406337321.

Subproblem 1
x + 23.4 = 28.406337321

Simplifying
x + 23.4 = 28.406337321

Reorder the terms:
23.4 + x = 28.406337321

Solving
23.4 + x = 28.406337321

Solving for variable 'x'.

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

Add '-23.4' to each side of the equation.
23.4 + -23.4 + x = 28.406337321 + -23.4

Combine like terms: 23.4 + -23.4 = 0.0
0.0 + x = 28.406337321 + -23.4
x = 28.406337321 + -23.4

Combine like terms: 28.406337321 + -23.4 = 5.006337321
x = 5.006337321

Simplifying
x = 5.006337321

Subproblem 2
x + 23.4 = -28.406337321

Simplifying
x + 23.4 = -28.406337321

Reorder the terms:
23.4 + x = -28.406337321

Solving
23.4 + x = -28.406337321

Solving for variable 'x'.

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

Add '-23.4' to each side of the equation.
23.4 + -23.4 + x = -28.406337321 + -23.4

Combine like terms: 23.4 + -23.4 = 0.0
0.0 + x = -28.406337321 + -23.4
x = -28.406337321 + -23.4

Combine like terms: -28.406337321 + -23.4 = -51.806337321
x = -51.806337321

Simplifying
x = -51.806337321

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.006337321, -51.806337321}