150+15x=80x-x^2

Solution for 150+15x=80x-x^2 equation:

Simplifying
150 + 15x = 80x + -1x2

Solving
150 + 15x = 80x + -1x2

Solving for variable 'x'.

Combine like terms: 15x + -80x = -65x
150 + -65x + x2 = 80x + -1x2 + -80x + x2

Reorder the terms:
150 + -65x + x2 = 80x + -80x + -1x2 + x2

Combine like terms: 80x + -80x = 0
150 + -65x + x2 = 0 + -1x2 + x2
150 + -65x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
150 + -65x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-150' to each side of the equation.
150 + -65x + -150 + x2 = 0 + -150

Reorder the terms:
150 + -150 + -65x + x2 = 0 + -150

Combine like terms: 150 + -150 = 0
0 + -65x + x2 = 0 + -150
-65x + x2 = 0 + -150

Combine like terms: 0 + -150 = -150
-65x + x2 = -150

The x term is -65x.  Take half its coefficient (-32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
-65x + 1056.25 + x2 = -150 + 1056.25

Reorder the terms:
1056.25 + -65x + x2 = -150 + 1056.25

Combine like terms: -150 + 1056.25 = 906.25
1056.25 + -65x + x2 = 906.25

Factor a perfect square on the left side:
(x + -32.5)(x + -32.5) = 906.25

Calculate the square root of the right side: 30.103986447

Break this problem into two subproblems by setting 
(x + -32.5) equal to 30.103986447 and -30.103986447.

Subproblem 1
x + -32.5 = 30.103986447

Simplifying
x + -32.5 = 30.103986447

Reorder the terms:
-32.5 + x = 30.103986447

Solving
-32.5 + x = 30.103986447

Solving for variable 'x'.

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

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = 30.103986447 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = 30.103986447 + 32.5
x = 30.103986447 + 32.5

Combine like terms: 30.103986447 + 32.5 = 62.603986447
x = 62.603986447

Simplifying
x = 62.603986447

Subproblem 2
x + -32.5 = -30.103986447

Simplifying
x + -32.5 = -30.103986447

Reorder the terms:
-32.5 + x = -30.103986447

Solving
-32.5 + x = -30.103986447

Solving for variable 'x'.

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

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = -30.103986447 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = -30.103986447 + 32.5
x = -30.103986447 + 32.5

Combine like terms: -30.103986447 + 32.5 = 2.396013553
x = 2.396013553

Simplifying
x = 2.396013553

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {62.603986447, 2.396013553}