-5x^2+30x-43=0

Solution for -5x^2+30x-43=0 equation:

Simplifying
-5x2 + 30x + -43 = 0

Reorder the terms:
-43 + 30x + -5x2 = 0

Solving
-43 + 30x + -5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
8.6 + -6x + x2 = 0

Move the constant term to the right:

Add '-8.6' to each side of the equation.
8.6 + -6x + -8.6 + x2 = 0 + -8.6

Reorder the terms:
8.6 + -8.6 + -6x + x2 = 0 + -8.6

Combine like terms: 8.6 + -8.6 = 0.0
0.0 + -6x + x2 = 0 + -8.6
-6x + x2 = 0 + -8.6

Combine like terms: 0 + -8.6 = -8.6
-6x + x2 = -8.6

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -8.6 + 9

Reorder the terms:
9 + -6x + x2 = -8.6 + 9

Combine like terms: -8.6 + 9 = 0.4
9 + -6x + x2 = 0.4

Factor a perfect square on the left side:
(x + -3)(x + -3) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(x + -3) equal to 0.632455532 and -0.632455532.

Subproblem 1
x + -3 = 0.632455532

Simplifying
x + -3 = 0.632455532

Reorder the terms:
-3 + x = 0.632455532

Solving
-3 + x = 0.632455532

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 0.632455532 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0.632455532 + 3
x = 0.632455532 + 3

Combine like terms: 0.632455532 + 3 = 3.632455532
x = 3.632455532

Simplifying
x = 3.632455532

Subproblem 2
x + -3 = -0.632455532

Simplifying
x + -3 = -0.632455532

Reorder the terms:
-3 + x = -0.632455532

Solving
-3 + x = -0.632455532

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -0.632455532 + 3

Combine like terms: -3 + 3 = 0
0 + x = -0.632455532 + 3
x = -0.632455532 + 3

Combine like terms: -0.632455532 + 3 = 2.367544468
x = 2.367544468

Simplifying
x = 2.367544468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.632455532, 2.367544468}