Find the Discriminant 7x^2+8x+5=0

$7 x^{2} + 8 x + 5 = 0$

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 $c$ .

$8^{2} - 4 (7 \cdot 5)$

Step 3

Evaluate the result to find the discriminant.

Simplify each term.

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

$64 - 4 (7 \cdot 5)$

Multiply $- 4 (7 \cdot 5)$ .

Multiply $7$ by $5$ .

$64 - 4 \cdot 35$

Multiply $- 4$ by $35$ .

$64 - 140$

Subtract $140$ from $64$ .

$- 76$