5x-6=x^2+90

Solution for 5x-6=x^2+90 equation:

Simplifying
5x + -6 = x2 + 90

Reorder the terms:
-6 + 5x = x2 + 90

Reorder the terms:
-6 + 5x = 90 + x2

Solving
-6 + 5x = 90 + x2

Solving for variable 'x'.

Reorder the terms:
-6 + -90 + 5x + -1x2 = 90 + x2 + -90 + -1x2

Combine like terms: -6 + -90 = -96
-96 + 5x + -1x2 = 90 + x2 + -90 + -1x2

Reorder the terms:
-96 + 5x + -1x2 = 90 + -90 + x2 + -1x2

Combine like terms: 90 + -90 = 0
-96 + 5x + -1x2 = 0 + x2 + -1x2
-96 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-96 + 5x + -1x2 = 0

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

Divide each side by '-1'.
96 + -5x + x2 = 0

Move the constant term to the right:

Add '-96' to each side of the equation.
96 + -5x + -96 + x2 = 0 + -96

Reorder the terms:
96 + -96 + -5x + x2 = 0 + -96

Combine like terms: 96 + -96 = 0
0 + -5x + x2 = 0 + -96
-5x + x2 = 0 + -96

Combine like terms: 0 + -96 = -96
-5x + x2 = -96

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 = -96 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -96 + 6.25

Combine like terms: -96 + 6.25 = -89.75
6.25 + -5x + x2 = -89.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = -89.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.