-4.5x^2+180x+60=0

Solution for -4.5x^2+180x+60=0 equation:

Simplifying
-4.5x2 + 180x + 60 = 0

Reorder the terms:
60 + 180x + -4.5x2 = 0

Solving
60 + 180x + -4.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.5 the coefficient of the squared term: 

Divide each side by '-4.5'.
-13.33333333 + -40x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -40x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -40x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -40x + x2 = 0 + 13.33333333
-40x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-40x + x2 = 13.33333333

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 13.33333333 + 400

Reorder the terms:
400 + -40x + x2 = 13.33333333 + 400

Combine like terms: 13.33333333 + 400 = 413.33333333
400 + -40x + x2 = 413.33333333

Factor a perfect square on the left side:
(x + -20)(x + -20) = 413.33333333

Calculate the square root of the right side: 20.330600909

Break this problem into two subproblems by setting 
(x + -20) equal to 20.330600909 and -20.330600909.

Subproblem 1
x + -20 = 20.330600909

Simplifying
x + -20 = 20.330600909

Reorder the terms:
-20 + x = 20.330600909

Solving
-20 + x = 20.330600909

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 20.330600909 + 20

Combine like terms: -20 + 20 = 0
0 + x = 20.330600909 + 20
x = 20.330600909 + 20

Combine like terms: 20.330600909 + 20 = 40.330600909
x = 40.330600909

Simplifying
x = 40.330600909

Subproblem 2
x + -20 = -20.330600909

Simplifying
x + -20 = -20.330600909

Reorder the terms:
-20 + x = -20.330600909

Solving
-20 + x = -20.330600909

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -20.330600909 + 20

Combine like terms: -20 + 20 = 0
0 + x = -20.330600909 + 20
x = -20.330600909 + 20

Combine like terms: -20.330600909 + 20 = -0.330600909
x = -0.330600909

Simplifying
x = -0.330600909

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {40.330600909, -0.330600909}