Find the Discriminant x^2+11x-48=3x

$x^{2} + 11 x - 48 = 3 x$

Step 1

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

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

$x^{2} + 11 x - 48 - 3 x = 0$

Subtract $3 x$ from $11 x$ .

$x^{2} + 8 x - 48 = 0$

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 $c$ .

$8^{2} - 4 (1 \cdot - 48)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $8$ to the power of $2$ .

$64 - 4 (1 \cdot - 48)$

Multiply $- 4 (1 \cdot - 48)$ .

Multiply $- 48$ by $1$ .

$64 - 4 \cdot - 48$

Multiply $- 4$ by $- 48$ .

$64 + 192$

Add $64$ and $192$ .

$256$