4x^2-23+51=5x+6

Solution for 4x^2-23+51=5x+6 equation:

Simplifying
4x2 + -23 + 51 = 5x + 6

Reorder the terms:
-23 + 51 + 4x2 = 5x + 6

Combine like terms: -23 + 51 = 28
28 + 4x2 = 5x + 6

Reorder the terms:
28 + 4x2 = 6 + 5x

Solving
28 + 4x2 = 6 + 5x

Solving for variable 'x'.

Reorder the terms:
28 + -6 + -5x + 4x2 = 6 + 5x + -6 + -5x

Combine like terms: 28 + -6 = 22
22 + -5x + 4x2 = 6 + 5x + -6 + -5x

Reorder the terms:
22 + -5x + 4x2 = 6 + -6 + 5x + -5x

Combine like terms: 6 + -6 = 0
22 + -5x + 4x2 = 0 + 5x + -5x
22 + -5x + 4x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
22 + -5x + 4x2 = 0

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

Divide each side by '4'.
5.5 + -1.25x + x2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + -1.25x + -5.5 + x2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + -1.25x + x2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + -1.25x + x2 = 0 + -5.5
-1.25x + x2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
-1.25x + x2 = -5.5

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = -5.5 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = -5.5 + 0.390625

Combine like terms: -5.5 + 0.390625 = -5.109375
0.390625 + -1.25x + x2 = -5.109375

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = -5.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.