-16x^2+290x-104=0

Solution for -16x^2+290x-104=0 equation:

Simplifying
-16x2 + 290x + -104 = 0

Reorder the terms:
-104 + 290x + -16x2 = 0

Solving
-104 + 290x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-52 + 145x + -8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-52 + 145x + -8x2)' equal to zero and attempt to solve:

Simplifying
-52 + 145x + -8x2 = 0

Solving
-52 + 145x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
6.5 + -18.125x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + -18.125x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + -18.125x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + -18.125x + x2 = 0 + -6.5
-18.125x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
-18.125x + x2 = -6.5

The x term is -18.125x.  Take half its coefficient (-9.0625).
Square it (82.12890625) and add it to both sides.

Add '82.12890625' to each side of the equation.
-18.125x + 82.12890625 + x2 = -6.5 + 82.12890625

Reorder the terms:
82.12890625 + -18.125x + x2 = -6.5 + 82.12890625

Combine like terms: -6.5 + 82.12890625 = 75.62890625
82.12890625 + -18.125x + x2 = 75.62890625

Factor a perfect square on the left side:
(x + -9.0625)(x + -9.0625) = 75.62890625

Calculate the square root of the right side: 8.696488156

Break this problem into two subproblems by setting 
(x + -9.0625) equal to 8.696488156 and -8.696488156.

Subproblem 1
x + -9.0625 = 8.696488156

Simplifying
x + -9.0625 = 8.696488156

Reorder the terms:
-9.0625 + x = 8.696488156

Solving
-9.0625 + x = 8.696488156

Solving for variable 'x'.

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

Add '9.0625' to each side of the equation.
-9.0625 + 9.0625 + x = 8.696488156 + 9.0625

Combine like terms: -9.0625 + 9.0625 = 0.0000
0.0000 + x = 8.696488156 + 9.0625
x = 8.696488156 + 9.0625

Combine like terms: 8.696488156 + 9.0625 = 17.758988156
x = 17.758988156

Simplifying
x = 17.758988156

Subproblem 2
x + -9.0625 = -8.696488156

Simplifying
x + -9.0625 = -8.696488156

Reorder the terms:
-9.0625 + x = -8.696488156

Solving
-9.0625 + x = -8.696488156

Solving for variable 'x'.

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

Add '9.0625' to each side of the equation.
-9.0625 + 9.0625 + x = -8.696488156 + 9.0625

Combine like terms: -9.0625 + 9.0625 = 0.0000
0.0000 + x = -8.696488156 + 9.0625
x = -8.696488156 + 9.0625

Combine like terms: -8.696488156 + 9.0625 = 0.366011844
x = 0.366011844

Simplifying
x = 0.366011844

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.758988156, 0.366011844}
Solution
x = {17.758988156, 0.366011844}