-3x^2+15x+12.5=0

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Solution for -3x^2+15x+12.5=0 equation: 


Simplifying
-3x2 + 15x + 12.5 = 0

Reorder the terms:
12.5 + 15x + -3x2 = 0

Solving
12.5 + 15x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-4.166666667 + -5x + x2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + -5x + 4.166666667 + x2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + -5x + x2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + -5x + x2 = 0 + 4.166666667
-5x + x2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
-5x + x2 = 4.166666667

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 4.166666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 4.166666667 + 6.25

Combine like terms: 4.166666667 + 6.25 = 10.416666667
6.25 + -5x + x2 = 10.416666667

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 10.416666667

Calculate the square root of the right side: 3.227486122

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.227486122 and -3.227486122.


Subproblem 1
x + -2.5 = 3.227486122

Simplifying
x + -2.5 = 3.227486122

Reorder the terms:
-2.5 + x = 3.227486122

Solving
-2.5 + x = 3.227486122

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.227486122 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.227486122 + 2.5
x = 3.227486122 + 2.5

Combine like terms: 3.227486122 + 2.5 = 5.727486122
x = 5.727486122

Simplifying
x = 5.727486122


Subproblem 2
x + -2.5 = -3.227486122

Simplifying
x + -2.5 = -3.227486122

Reorder the terms:
-2.5 + x = -3.227486122

Solving
-2.5 + x = -3.227486122

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.227486122 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.227486122 + 2.5
x = -3.227486122 + 2.5

Combine like terms: -3.227486122 + 2.5 = -0.727486122
x = -0.727486122

Simplifying
x = -0.727486122


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.727486122, -0.727486122}

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