3x-4=2x^2+x+1

Solution for 3x-4=2x^2+x+1 equation:

Simplifying
3x + -4 = 2x2 + x + 1

Reorder the terms:
-4 + 3x = 2x2 + x + 1

Reorder the terms:
-4 + 3x = 1 + x + 2x2

Solving
-4 + 3x = 1 + x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -1 + 3x + -1x + -2x2 = 1 + x + 2x2 + -1 + -1x + -2x2

Combine like terms: -4 + -1 = -5
-5 + 3x + -1x + -2x2 = 1 + x + 2x2 + -1 + -1x + -2x2

Combine like terms: 3x + -1x = 2x
-5 + 2x + -2x2 = 1 + x + 2x2 + -1 + -1x + -2x2

Reorder the terms:
-5 + 2x + -2x2 = 1 + -1 + x + -1x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
-5 + 2x + -2x2 = 0 + x + -1x + 2x2 + -2x2
-5 + 2x + -2x2 = x + -1x + 2x2 + -2x2

Combine like terms: x + -1x = 0
-5 + 2x + -2x2 = 0 + 2x2 + -2x2
-5 + 2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 2x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
2.5 + -1x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -1x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -1x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -1x + x2 = 0 + -2.5
-1x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-1x + x2 = -2.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -2.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + -1x + x2 = -2.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.