(45x-.3x^2)-(7x+13)=

Solution for (45x-.3x^2)-(7x+13)= equation:

Simplifying
(45x + -0.3x2) + -1(7x + 13) = 0

Remove parenthesis around (45x + -0.3x2)
45x + -0.3x2 + -1(7x + 13) = 0

Reorder the terms:
45x + -0.3x2 + -1(13 + 7x) = 0
45x + -0.3x2 + (13 * -1 + 7x * -1) = 0
45x + -0.3x2 + (-13 + -7x) = 0

Reorder the terms:
-13 + 45x + -7x + -0.3x2 = 0

Combine like terms: 45x + -7x = 38x
-13 + 38x + -0.3x2 = 0

Solving
-13 + 38x + -0.3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
43.33333333 + -126.6666667x + x2 = 0

Move the constant term to the right:

Add '-43.33333333' to each side of the equation.
43.33333333 + -126.6666667x + -43.33333333 + x2 = 0 + -43.33333333

Reorder the terms:
43.33333333 + -43.33333333 + -126.6666667x + x2 = 0 + -43.33333333

Combine like terms: 43.33333333 + -43.33333333 = 0.00000000
0.00000000 + -126.6666667x + x2 = 0 + -43.33333333
-126.6666667x + x2 = 0 + -43.33333333

Combine like terms: 0 + -43.33333333 = -43.33333333
-126.6666667x + x2 = -43.33333333

The x term is -126.6666667x.  Take half its coefficient (-63.33333335).
Square it (4011.111113) and add it to both sides.

Add '4011.111113' to each side of the equation.
-126.6666667x + 4011.111113 + x2 = -43.33333333 + 4011.111113

Reorder the terms:
4011.111113 + -126.6666667x + x2 = -43.33333333 + 4011.111113

Combine like terms: -43.33333333 + 4011.111113 = 3967.77777967
4011.111113 + -126.6666667x + x2 = 3967.77777967

Factor a perfect square on the left side:
(x + -63.33333335)(x + -63.33333335) = 3967.77777967

Calculate the square root of the right side: 62.990299092

Break this problem into two subproblems by setting 
(x + -63.33333335) equal to 62.990299092 and -62.990299092.

Subproblem 1
x + -63.33333335 = 62.990299092

Simplifying
x + -63.33333335 = 62.990299092

Reorder the terms:
-63.33333335 + x = 62.990299092

Solving
-63.33333335 + x = 62.990299092

Solving for variable 'x'.

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

Add '63.33333335' to each side of the equation.
-63.33333335 + 63.33333335 + x = 62.990299092 + 63.33333335

Combine like terms: -63.33333335 + 63.33333335 = 0.00000000
0.00000000 + x = 62.990299092 + 63.33333335
x = 62.990299092 + 63.33333335

Combine like terms: 62.990299092 + 63.33333335 = 126.323632442
x = 126.323632442

Simplifying
x = 126.323632442

Subproblem 2
x + -63.33333335 = -62.990299092

Simplifying
x + -63.33333335 = -62.990299092

Reorder the terms:
-63.33333335 + x = -62.990299092

Solving
-63.33333335 + x = -62.990299092

Solving for variable 'x'.

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

Add '63.33333335' to each side of the equation.
-63.33333335 + 63.33333335 + x = -62.990299092 + 63.33333335

Combine like terms: -63.33333335 + 63.33333335 = 0.00000000
0.00000000 + x = -62.990299092 + 63.33333335
x = -62.990299092 + 63.33333335

Combine like terms: -62.990299092 + 63.33333335 = 0.343034258
x = 0.343034258

Simplifying
x = 0.343034258

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {126.323632442, 0.343034258}