Find the Discriminant 5x^2-3x+4=0

$5 x^{2} - 3 x + 4 = 0$

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 $c$ .

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

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$9 - 4 (5 \cdot 4)$

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

Multiply $5$ by $4$ .

$9 - 4 \cdot 20$

Multiply $- 4$ by $20$ .

$9 - 80$

Subtract $80$ from $9$ .

$- 71$