19x^2-60x-3=0

Solution for 19x^2-60x-3=0 equation:

Simplifying
19x2 + -60x + -3 = 0

Reorder the terms:
-3 + -60x + 19x2 = 0

Solving
-3 + -60x + 19x2 = 0

Solving for variable 'x'.

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

Divide each side by '19'.
-0.1578947368 + -3.157894737x + x2 = 0

Move the constant term to the right:

Add '0.1578947368' to each side of the equation.
-0.1578947368 + -3.157894737x + 0.1578947368 + x2 = 0 + 0.1578947368

Reorder the terms:
-0.1578947368 + 0.1578947368 + -3.157894737x + x2 = 0 + 0.1578947368

Combine like terms: -0.1578947368 + 0.1578947368 = 0.0000000000
0.0000000000 + -3.157894737x + x2 = 0 + 0.1578947368
-3.157894737x + x2 = 0 + 0.1578947368

Combine like terms: 0 + 0.1578947368 = 0.1578947368
-3.157894737x + x2 = 0.1578947368

The x term is -3.157894737x.  Take half its coefficient (-1.578947369).
Square it (2.493074794) and add it to both sides.

Add '2.493074794' to each side of the equation.
-3.157894737x + 2.493074794 + x2 = 0.1578947368 + 2.493074794

Reorder the terms:
2.493074794 + -3.157894737x + x2 = 0.1578947368 + 2.493074794

Combine like terms: 0.1578947368 + 2.493074794 = 2.6509695308
2.493074794 + -3.157894737x + x2 = 2.6509695308

Factor a perfect square on the left side:
(x + -1.578947369)(x + -1.578947369) = 2.6509695308

Calculate the square root of the right side: 1.628179821

Break this problem into two subproblems by setting 
(x + -1.578947369) equal to 1.628179821 and -1.628179821.

Subproblem 1
x + -1.578947369 = 1.628179821

Simplifying
x + -1.578947369 = 1.628179821

Reorder the terms:
-1.578947369 + x = 1.628179821

Solving
-1.578947369 + x = 1.628179821

Solving for variable 'x'.

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

Add '1.578947369' to each side of the equation.
-1.578947369 + 1.578947369 + x = 1.628179821 + 1.578947369

Combine like terms: -1.578947369 + 1.578947369 = 0.000000000
0.000000000 + x = 1.628179821 + 1.578947369
x = 1.628179821 + 1.578947369

Combine like terms: 1.628179821 + 1.578947369 = 3.20712719
x = 3.20712719

Simplifying
x = 3.20712719

Subproblem 2
x + -1.578947369 = -1.628179821

Simplifying
x + -1.578947369 = -1.628179821

Reorder the terms:
-1.578947369 + x = -1.628179821

Solving
-1.578947369 + x = -1.628179821

Solving for variable 'x'.

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

Add '1.578947369' to each side of the equation.
-1.578947369 + 1.578947369 + x = -1.628179821 + 1.578947369

Combine like terms: -1.578947369 + 1.578947369 = 0.000000000
0.000000000 + x = -1.628179821 + 1.578947369
x = -1.628179821 + 1.578947369

Combine like terms: -1.628179821 + 1.578947369 = -0.049232452
x = -0.049232452

Simplifying
x = -0.049232452

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.20712719, -0.049232452}