-25X^2+650X+51000=0

Solution for -25X^2+650X+51000=0 equation:

Simplifying
-25X2 + 650X + 51000 = 0

Reorder the terms:
51000 + 650X + -25X2 = 0

Solving
51000 + 650X + -25X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '25'.
25(2040 + 26X + -1X2) = 0

Factor a trinomial.
25((60 + -1X)(34 + X)) = 0

Ignore the factor 25.
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 '(34 + X)' equal to zero and attempt to solve:

Simplifying
34 + X = 0

Solving
34 + X = 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 + X = 0 + -34

Combine like terms: 34 + -34 = 0
0 + X = 0 + -34
X = 0 + -34

Combine like terms: 0 + -34 = -34
X = -34

Simplifying
X = -34
Solution
X = {60, -34}