Find the Discriminant 5x^2-3x+6=0

$5 x^{2} - 3 x + 6 = 0$

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 $c$ .

${(- 3)}^{2} - 4 (5 \cdot 6)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

Raise $- 3$ to the power of $2$ .

$9 - 4 (5 \cdot 6)$

Multiply $- 4 (5 \cdot 6)$ .

Multiply $5$ by $6$ .

$9 - 4 \cdot 30$

Multiply $- 4$ by $30$ .

$9 - 120$

Subtract $120$ from $9$ .

$- 111$