2x^2=3+x

Solution for 2x^2=3+x equation:

Simplifying
2x2 = 3 + x

Solving
2x2 = 3 + x

Solving for variable 'x'.

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

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

Combine like terms: 3 + -3 = 0
-3 + -1x + 2x2 = 0 + x + -1x
-3 + -1x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + -1x + 2x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1, 1.5}