3x^2-90x+240=0

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Solution for 3x^2-90x+240=0 equation: 


Simplifying
3x2 + -90x + 240 = 0

Reorder the terms:
240 + -90x + 3x2 = 0

Solving
240 + -90x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(80 + -30x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(80 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
80 + -30x + x2 = 0

Solving
80 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-80' to each side of the equation.
80 + -30x + -80 + x2 = 0 + -80

Reorder the terms:
80 + -80 + -30x + x2 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -30x + x2 = 0 + -80
-30x + x2 = 0 + -80

Combine like terms: 0 + -80 = -80
-30x + x2 = -80

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = -80 + 225

Reorder the terms:
225 + -30x + x2 = -80 + 225

Combine like terms: -80 + 225 = 145
225 + -30x + x2 = 145

Factor a perfect square on the left side:
(x + -15)(x + -15) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(x + -15) equal to 12.041594579 and -12.041594579.


Subproblem 1
x + -15 = 12.041594579

Simplifying
x + -15 = 12.041594579

Reorder the terms:
-15 + x = 12.041594579

Solving
-15 + x = 12.041594579

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 12.041594579 + 15

Combine like terms: -15 + 15 = 0
0 + x = 12.041594579 + 15
x = 12.041594579 + 15

Combine like terms: 12.041594579 + 15 = 27.041594579
x = 27.041594579

Simplifying
x = 27.041594579


Subproblem 2
x + -15 = -12.041594579

Simplifying
x + -15 = -12.041594579

Reorder the terms:
-15 + x = -12.041594579

Solving
-15 + x = -12.041594579

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -12.041594579 + 15

Combine like terms: -15 + 15 = 0
0 + x = -12.041594579 + 15
x = -12.041594579 + 15

Combine like terms: -12.041594579 + 15 = 2.958405421
x = 2.958405421

Simplifying
x = 2.958405421


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.041594579, 2.958405421}
Solution
x = {27.041594579, 2.958405421}

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