Find the Discriminant 8=12x-3x^2

$8 = 12 x - 3 x^{2}$

Step 1

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

Subtract $12 x$ from both sides of the equation.

$8 - 12 x = - 3 x^{2}$

Add $3 x^{2}$ to both sides of the equation.

$8 - 12 x + 3 x^{2} = 0$

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 $c$ .

${(- 12)}^{2} - 4 (3 \cdot 8)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$144 - 4 (3 \cdot 8)$

Multiply $- 4 (3 \cdot 8)$ .

Multiply $3$ by $8$ .

$144 - 4 \cdot 24$

Multiply $- 4$ by $24$ .

$144 - 96$

Subtract $96$ from $144$ .

$48$