6x^2-15x=125(3.14)

Solution for 6x^2-15x=125(3.14) equation:

Simplifying
6x2 + -15x = 125(3.14)

Reorder the terms:
-15x + 6x2 = 125(3.14)

Multiply 125 * 3.14
-15x + 6x2 = 392.5

Solving
-15x + 6x2 = 392.5

Solving for variable 'x'.

Reorder the terms:
-392.5 + -15x + 6x2 = 392.5 + -392.5

Combine like terms: 392.5 + -392.5 = 0.0
-392.5 + -15x + 6x2 = 0.0

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

Divide each side by '6'.
-65.41666667 + -2.5x + x2 = 0.0

Move the constant term to the right:

Add '65.41666667' to each side of the equation.
-65.41666667 + -2.5x + 65.41666667 + x2 = 0.0 + 65.41666667

Reorder the terms:
-65.41666667 + 65.41666667 + -2.5x + x2 = 0.0 + 65.41666667

Combine like terms: -65.41666667 + 65.41666667 = 0.00000000
0.00000000 + -2.5x + x2 = 0.0 + 65.41666667
-2.5x + x2 = 0.0 + 65.41666667

Combine like terms: 0.0 + 65.41666667 = 65.41666667
-2.5x + x2 = 65.41666667

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 = 65.41666667 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 65.41666667 + 1.5625

Combine like terms: 65.41666667 + 1.5625 = 66.97916667
1.5625 + -2.5x + x2 = 66.97916667

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 66.97916667

Calculate the square root of the right side: 8.184080075

Break this problem into two subproblems by setting 
(x + -1.25) equal to 8.184080075 and -8.184080075.

Subproblem 1
x + -1.25 = 8.184080075

Simplifying
x + -1.25 = 8.184080075

Reorder the terms:
-1.25 + x = 8.184080075

Solving
-1.25 + x = 8.184080075

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 = 8.184080075 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 8.184080075 + 1.25
x = 8.184080075 + 1.25

Combine like terms: 8.184080075 + 1.25 = 9.434080075
x = 9.434080075

Simplifying
x = 9.434080075

Subproblem 2
x + -1.25 = -8.184080075

Simplifying
x + -1.25 = -8.184080075

Reorder the terms:
-1.25 + x = -8.184080075

Solving
-1.25 + x = -8.184080075

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 = -8.184080075 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -8.184080075 + 1.25
x = -8.184080075 + 1.25

Combine like terms: -8.184080075 + 1.25 = -6.934080075
x = -6.934080075

Simplifying
x = -6.934080075

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.434080075, -6.934080075}