2x^2+80x+20000=22400

Solution for 2x^2+80x+20000=22400 equation:

Simplifying
2x2 + 80x + 20000 = 22400

Reorder the terms:
20000 + 80x + 2x2 = 22400

Solving
20000 + 80x + 2x2 = 22400

Solving for variable 'x'.

Reorder the terms:
20000 + -22400 + 80x + 2x2 = 22400 + -22400

Combine like terms: 20000 + -22400 = -2400
-2400 + 80x + 2x2 = 22400 + -22400

Combine like terms: 22400 + -22400 = 0
-2400 + 80x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1200 + 40x + x2) = 0

Factor a trinomial.
2((-60 + -1x)(20 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-60 + -1x)' equal to zero and attempt to solve:

Simplifying
-60 + -1x = 0

Solving
-60 + -1x = 0

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

Add '60' to each side of the equation.
-60 + 60 + -1x = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -1x = 0 + 60
-1x = 0 + 60

Combine like terms: 0 + 60 = 60
-1x = 60

Divide each side by '-1'.
x = -60

Simplifying
x = -60
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-60, 20}