-2x^2+3390x-67730=0

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Solution for -2x^2+3390x-67730=0 equation: 


Simplifying
-2x2 + 3390x + -67730 = 0

Reorder the terms:
-67730 + 3390x + -2x2 = 0

Solving
-67730 + 3390x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-33865 + 1695x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-33865 + 1695x + -1x2)' equal to zero and attempt to solve:

Simplifying
-33865 + 1695x + -1x2 = 0

Solving
-33865 + 1695x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
33865 + -1695x + x2 = 0

Move the constant term to the right:

Add '-33865' to each side of the equation.
33865 + -1695x + -33865 + x2 = 0 + -33865

Reorder the terms:
33865 + -33865 + -1695x + x2 = 0 + -33865

Combine like terms: 33865 + -33865 = 0
0 + -1695x + x2 = 0 + -33865
-1695x + x2 = 0 + -33865

Combine like terms: 0 + -33865 = -33865
-1695x + x2 = -33865

The x term is -1695x.  Take half its coefficient (-847.5).
Square it (718256.25) and add it to both sides.

Add '718256.25' to each side of the equation.
-1695x + 718256.25 + x2 = -33865 + 718256.25

Reorder the terms:
718256.25 + -1695x + x2 = -33865 + 718256.25

Combine like terms: -33865 + 718256.25 = 684391.25
718256.25 + -1695x + x2 = 684391.25

Factor a perfect square on the left side:
(x + -847.5)(x + -847.5) = 684391.25

Calculate the square root of the right side: 827.279426796

Break this problem into two subproblems by setting 
(x + -847.5) equal to 827.279426796 and -827.279426796.


Subproblem 1
x + -847.5 = 827.279426796

Simplifying
x + -847.5 = 827.279426796

Reorder the terms:
-847.5 + x = 827.279426796

Solving
-847.5 + x = 827.279426796

Solving for variable 'x'.

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

Add '847.5' to each side of the equation.
-847.5 + 847.5 + x = 827.279426796 + 847.5

Combine like terms: -847.5 + 847.5 = 0.0
0.0 + x = 827.279426796 + 847.5
x = 827.279426796 + 847.5

Combine like terms: 827.279426796 + 847.5 = 1674.779426796
x = 1674.779426796

Simplifying
x = 1674.779426796


Subproblem 2
x + -847.5 = -827.279426796

Simplifying
x + -847.5 = -827.279426796

Reorder the terms:
-847.5 + x = -827.279426796

Solving
-847.5 + x = -827.279426796

Solving for variable 'x'.

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

Add '847.5' to each side of the equation.
-847.5 + 847.5 + x = -827.279426796 + 847.5

Combine like terms: -847.5 + 847.5 = 0.0
0.0 + x = -827.279426796 + 847.5
x = -827.279426796 + 847.5

Combine like terms: -827.279426796 + 847.5 = 20.220573204
x = 20.220573204

Simplifying
x = 20.220573204


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1674.779426796, 20.220573204}
Solution
x = {1674.779426796, 20.220573204}

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