15x^2-145x+90=29x

Solution for 15x^2-145x+90=29x equation:

Simplifying
15x2 + -145x + 90 = 29x

Reorder the terms:
90 + -145x + 15x2 = 29x

Solving
90 + -145x + 15x2 = 29x

Solving for variable 'x'.

Reorder the terms:
90 + -145x + -29x + 15x2 = 29x + -29x

Combine like terms: -145x + -29x = -174x
90 + -174x + 15x2 = 29x + -29x

Combine like terms: 29x + -29x = 0
90 + -174x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + -58x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(30 + -58x + 5x2)' equal to zero and attempt to solve:

Simplifying
30 + -58x + 5x2 = 0

Solving
30 + -58x + 5x2 = 0

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

Divide each side by '5'.
6 + -11.6x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -11.6x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -11.6x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -11.6x + x2 = 0 + -6
-11.6x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-11.6x + x2 = -6

The x term is -11.6x.  Take half its coefficient (-5.8).
Square it (33.64) and add it to both sides.

Add '33.64' to each side of the equation.
-11.6x + 33.64 + x2 = -6 + 33.64

Reorder the terms:
33.64 + -11.6x + x2 = -6 + 33.64

Combine like terms: -6 + 33.64 = 27.64
33.64 + -11.6x + x2 = 27.64

Factor a perfect square on the left side:
(x + -5.8)(x + -5.8) = 27.64

Calculate the square root of the right side: 5.257375771

Break this problem into two subproblems by setting 
(x + -5.8) equal to 5.257375771 and -5.257375771.

Subproblem 1
x + -5.8 = 5.257375771

Simplifying
x + -5.8 = 5.257375771

Reorder the terms:
-5.8 + x = 5.257375771

Solving
-5.8 + x = 5.257375771

Solving for variable 'x'.

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

Add '5.8' to each side of the equation.
-5.8 + 5.8 + x = 5.257375771 + 5.8

Combine like terms: -5.8 + 5.8 = 0.0
0.0 + x = 5.257375771 + 5.8
x = 5.257375771 + 5.8

Combine like terms: 5.257375771 + 5.8 = 11.057375771
x = 11.057375771

Simplifying
x = 11.057375771

Subproblem 2
x + -5.8 = -5.257375771

Simplifying
x + -5.8 = -5.257375771

Reorder the terms:
-5.8 + x = -5.257375771

Solving
-5.8 + x = -5.257375771

Solving for variable 'x'.

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

Add '5.8' to each side of the equation.
-5.8 + 5.8 + x = -5.257375771 + 5.8

Combine like terms: -5.8 + 5.8 = 0.0
0.0 + x = -5.257375771 + 5.8
x = -5.257375771 + 5.8

Combine like terms: -5.257375771 + 5.8 = 0.542624229
x = 0.542624229

Simplifying
x = 0.542624229

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.057375771, 0.542624229}
Solution
x = {11.057375771, 0.542624229}