Find the Discriminant x^2-9x+18=2x^2+3x-1

$x^{2} - 9 x + 18 = 2 x^{2} + 3 x - 1$

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $2 x^{2}$ from both sides of the equation.

$x^{2} - 9 x + 18 - 2 x^{2} = 3 x - 1$

Subtract $3 x$ from both sides of the equation.

$x^{2} - 9 x + 18 - 2 x^{2} - 3 x = - 1$

Add $1$ to both sides of the equation.

$x^{2} - 9 x + 18 - 2 x^{2} - 3 x + 1 = 0$

Simplify $x^{2} - 9 x + 18 - 2 x^{2} - 3 x + 1$ .

Subtract $2 x^{2}$ from $x^{2}$ .

$- x^{2} - 9 x + 18 - 3 x + 1 = 0$

Subtract $3 x$ from $- 9 x$ .

$- x^{2} - 12 x + 18 + 1 = 0$

Add $18$ and $1$ .

$- x^{2} - 12 x + 19 = 0$

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 12)}^{2} - 4 (- 1 \cdot 19)$

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 12$ to the power of $2$ .

$144 - 4 (- 1 \cdot 19)$

Multiply $- 1$ by $19$ .

$144 - 4 \cdot - 19$

Multiply $- 4$ by $- 19$ .

$144 + 76$

Add $144$ and $76$ .

$220$