50x^2+200x=51000

Solution for 50x^2+200x=51000 equation:

Simplifying
50x2 + 200x = 51000

Reorder the terms:
200x + 50x2 = 51000

Solving
200x + 50x2 = 51000

Solving for variable 'x'.

Reorder the terms:
-51000 + 200x + 50x2 = 51000 + -51000

Combine like terms: 51000 + -51000 = 0
-51000 + 200x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '50'.
50(-1020 + 4x + x2) = 0

Factor a trinomial.
50((-34 + -1x)(30 + -1x)) = 0

Ignore the factor 50.
Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve:

Simplifying
-34 + -1x = 0

Solving
-34 + -1x = 0

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

Add '34' to each side of the equation.
-34 + 34 + -1x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -1x = 0 + 34
-1x = 0 + 34

Combine like terms: 0 + 34 = 34
-1x = 34

Divide each side by '-1'.
x = -34

Simplifying
x = -34
Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-34, 30}