-60+620x+200x^2=0

Solution for -60+620x+200x^2=0 equation:

Simplifying
-60 + 620x + 200x2 = 0

Solving
-60 + 620x + 200x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-3 + 31x + 10x2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-3 + 31x + 10x2)' equal to zero and attempt to solve:

Simplifying
-3 + 31x + 10x2 = 0

Solving
-3 + 31x + 10x2 = 0

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

Divide each side by '10'.
-0.3 + 3.1x + x2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 3.1x + 0.3 + x2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 3.1x + x2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 3.1x + x2 = 0.0 + 0.3
3.1x + x2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
3.1x + x2 = 0.3

The x term is 3.1x.  Take half its coefficient (1.55).
Square it (2.4025) and add it to both sides.

Add '2.4025' to each side of the equation.
3.1x + 2.4025 + x2 = 0.3 + 2.4025

Reorder the terms:
2.4025 + 3.1x + x2 = 0.3 + 2.4025

Combine like terms: 0.3 + 2.4025 = 2.7025
2.4025 + 3.1x + x2 = 2.7025

Factor a perfect square on the left side:
(x + 1.55)(x + 1.55) = 2.7025

Calculate the square root of the right side: 1.643928222

Break this problem into two subproblems by setting 
(x + 1.55) equal to 1.643928222 and -1.643928222.

Subproblem 1
x + 1.55 = 1.643928222

Simplifying
x + 1.55 = 1.643928222

Reorder the terms:
1.55 + x = 1.643928222

Solving
1.55 + x = 1.643928222

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = 1.643928222 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = 1.643928222 + -1.55
x = 1.643928222 + -1.55

Combine like terms: 1.643928222 + -1.55 = 0.093928222
x = 0.093928222

Simplifying
x = 0.093928222

Subproblem 2
x + 1.55 = -1.643928222

Simplifying
x + 1.55 = -1.643928222

Reorder the terms:
1.55 + x = -1.643928222

Solving
1.55 + x = -1.643928222

Solving for variable 'x'.

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

Add '-1.55' to each side of the equation.
1.55 + -1.55 + x = -1.643928222 + -1.55

Combine like terms: 1.55 + -1.55 = 0.00
0.00 + x = -1.643928222 + -1.55
x = -1.643928222 + -1.55

Combine like terms: -1.643928222 + -1.55 = -3.193928222
x = -3.193928222

Simplifying
x = -3.193928222

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.093928222, -3.193928222}
Solution
x = {0.093928222, -3.193928222}