15x^2-35x-6=0

Solution for 15x^2-35x-6=0 equation:

Simplifying
15x2 + -35x + -6 = 0

Reorder the terms:
-6 + -35x + 15x2 = 0

Solving
-6 + -35x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-0.4 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -2.333333333x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -2.333333333x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -2.333333333x + x2 = 0 + 0.4
-2.333333333x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-2.333333333x + x2 = 0.4

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 0.4 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 0.4 + 1.361111112

Combine like terms: 0.4 + 1.361111112 = 1.761111112
1.361111112 + -2.333333333x + x2 = 1.761111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 1.761111112

Calculate the square root of the right side: 1.327068616

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.327068616 and -1.327068616.

Subproblem 1
x + -1.166666667 = 1.327068616

Simplifying
x + -1.166666667 = 1.327068616

Reorder the terms:
-1.166666667 + x = 1.327068616

Solving
-1.166666667 + x = 1.327068616

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 1.327068616 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 1.327068616 + 1.166666667
x = 1.327068616 + 1.166666667

Combine like terms: 1.327068616 + 1.166666667 = 2.493735283
x = 2.493735283

Simplifying
x = 2.493735283

Subproblem 2
x + -1.166666667 = -1.327068616

Simplifying
x + -1.166666667 = -1.327068616

Reorder the terms:
-1.166666667 + x = -1.327068616

Solving
-1.166666667 + x = -1.327068616

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -1.327068616 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -1.327068616 + 1.166666667
x = -1.327068616 + 1.166666667

Combine like terms: -1.327068616 + 1.166666667 = -0.160401949
x = -0.160401949

Simplifying
x = -0.160401949

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.493735283, -0.160401949}