Find the Discriminant 2x(x-3)=x+4

$2 x (x - 3) = x + 4$

Step 1

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

Simplify the left side.

Simplify $2 x (x - 3)$ .

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 3 = x + 4$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 3 = x + 4$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 3 = x + 4$

Multiply $- 3$ by $2$ .

$2 x^{2} - 6 x = x + 4$

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

Subtract $x$ from both sides of the equation.

$2 x^{2} - 6 x - x = 4$

Subtract $4$ from both sides of the equation.

$2 x^{2} - 6 x - x - 4 = 0$

Subtract $x$ from $- 6 x$ .

$2 x^{2} - 7 x - 4 = 0$

Step 2

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

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

Step 3

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

${(- 7)}^{2} - 4 (2 \cdot - 4)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 7$ to the power of $2$ .

$49 - 4 (2 \cdot - 4)$

Multiply $- 4 (2 \cdot - 4)$ .

Multiply $2$ by $- 4$ .

$49 - 4 \cdot - 8$

Multiply $- 4$ by $- 8$ .

$49 + 32$

Add $49$ and $32$ .

$81$