In the following, determine whether the given values are solutions of the given equation or not:
$2x^2\ –\ x\ +\ 9\ =\ x^2\ +\ 4x\ +\ 3,\ x\ =\ 2,\ x\ =\ 3$

Given:

The given equation is $2x^2\ –\ x\ +\ 9\ =\ x^2\ +\ 4x\ +\ 3$

To do:

We have to determine whether $x=2, x=3$ are solutions of the given equation.

Solution:

If the given values are the solutions of the given equation then they should satisfy the given equation.

Therefore,

For $x=2$,

LHS$=2x^2-x+9$

        $=2(2)^2-2+9$

        $=8-2+9$

       $=15$

RHS$=x^2+4x+3$

        $=(2)^2+4(2)+3$

        $=4+8+3$

        $=15$

LHS$=$RHS

Hence, $x=2$ is a solution of the given equation.

For $x=3$,

LHS$=2x^2-x+9$

        $=2(3)^2-3+9$

        $=18-3+9$

        $=24$

RHS$=x^2+4x+3$

        $=(3)^2+4(3)+3$

       $=9+12+3$

       $=24$

LHS$=$RHS

Hence, $x=3$ is a solution of the given equation.