90-3x^2=2x^2-25x

Solution for 90-3x^2=2x^2-25x equation:

Simplifying
90 + -3x2 = 2x2 + -25x

Reorder the terms:
90 + -3x2 = -25x + 2x2

Solving
90 + -3x2 = -25x + 2x2

Solving for variable 'x'.

Reorder the terms:
90 + 25x + -3x2 + -2x2 = -25x + 2x2 + 25x + -2x2

Combine like terms: -3x2 + -2x2 = -5x2
90 + 25x + -5x2 = -25x + 2x2 + 25x + -2x2

Reorder the terms:
90 + 25x + -5x2 = -25x + 25x + 2x2 + -2x2

Combine like terms: -25x + 25x = 0
90 + 25x + -5x2 = 0 + 2x2 + -2x2
90 + 25x + -5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
90 + 25x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(18 + 5x + -1x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(18 + 5x + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + 5x + -1x2 = 0

Solving
18 + 5x + -1x2 = 0

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

Divide each side by '-1'.
-18 + -5x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -5x + x2 = 0 + 18
-5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-5x + x2 = 18

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 18 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 18 + 6.25

Combine like terms: 18 + 6.25 = 24.25
6.25 + -5x + x2 = 24.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.924428901 and -4.924428901.

Subproblem 1
x + -2.5 = 4.924428901

Simplifying
x + -2.5 = 4.924428901

Reorder the terms:
-2.5 + x = 4.924428901

Solving
-2.5 + x = 4.924428901

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 4.924428901 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.924428901 + 2.5
x = 4.924428901 + 2.5

Combine like terms: 4.924428901 + 2.5 = 7.424428901
x = 7.424428901

Simplifying
x = 7.424428901

Subproblem 2
x + -2.5 = -4.924428901

Simplifying
x + -2.5 = -4.924428901

Reorder the terms:
-2.5 + x = -4.924428901

Solving
-2.5 + x = -4.924428901

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -4.924428901 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.924428901 + 2.5
x = -4.924428901 + 2.5

Combine like terms: -4.924428901 + 2.5 = -2.424428901
x = -2.424428901

Simplifying
x = -2.424428901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.424428901, -2.424428901}
Solution
x = {7.424428901, -2.424428901}