Find the Discriminant 3x^2-6x+7=0

$3 x^{2} - 6 x + 7 = 0$

Step 1

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

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

Step 2

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

${(- 6)}^{2} - 4 (3 \cdot 7)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 6$ to the power of $2$ .

$36 - 4 (3 \cdot 7)$

Multiply $- 4 (3 \cdot 7)$ .

Multiply $3$ by $7$ .

$36 - 4 \cdot 21$

Multiply $- 4$ by $21$ .

$36 - 84$

Subtract $84$ from $36$ .

$- 48$