-0.2x^2+90x-3000=0

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Solution for -0.2x^2+90x-3000=0 equation: 


Simplifying
-0.2x2 + 90x + -3000 = 0

Reorder the terms:
-3000 + 90x + -0.2x2 = 0

Solving
-3000 + 90x + -0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
15000 + -450x + x2 = 0

Move the constant term to the right:

Add '-15000' to each side of the equation.
15000 + -450x + -15000 + x2 = 0 + -15000

Reorder the terms:
15000 + -15000 + -450x + x2 = 0 + -15000

Combine like terms: 15000 + -15000 = 0
0 + -450x + x2 = 0 + -15000
-450x + x2 = 0 + -15000

Combine like terms: 0 + -15000 = -15000
-450x + x2 = -15000

The x term is -450x.  Take half its coefficient (-225).
Square it (50625) and add it to both sides.

Add '50625' to each side of the equation.
-450x + 50625 + x2 = -15000 + 50625

Reorder the terms:
50625 + -450x + x2 = -15000 + 50625

Combine like terms: -15000 + 50625 = 35625
50625 + -450x + x2 = 35625

Factor a perfect square on the left side:
(x + -225)(x + -225) = 35625

Calculate the square root of the right side: 188.745860882

Break this problem into two subproblems by setting 
(x + -225) equal to 188.745860882 and -188.745860882.


Subproblem 1
x + -225 = 188.745860882

Simplifying
x + -225 = 188.745860882

Reorder the terms:
-225 + x = 188.745860882

Solving
-225 + x = 188.745860882

Solving for variable 'x'.

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

Add '225' to each side of the equation.
-225 + 225 + x = 188.745860882 + 225

Combine like terms: -225 + 225 = 0
0 + x = 188.745860882 + 225
x = 188.745860882 + 225

Combine like terms: 188.745860882 + 225 = 413.745860882
x = 413.745860882

Simplifying
x = 413.745860882


Subproblem 2
x + -225 = -188.745860882

Simplifying
x + -225 = -188.745860882

Reorder the terms:
-225 + x = -188.745860882

Solving
-225 + x = -188.745860882

Solving for variable 'x'.

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

Add '225' to each side of the equation.
-225 + 225 + x = -188.745860882 + 225

Combine like terms: -225 + 225 = 0
0 + x = -188.745860882 + 225
x = -188.745860882 + 225

Combine like terms: -188.745860882 + 225 = 36.254139118
x = 36.254139118

Simplifying
x = 36.254139118


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {413.745860882, 36.254139118}

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