Find the Discriminant b^2-4ac=7

$b^{2} - 4 a c = 7$

Step 1

Subtract $7$ from both sides of the equation.

$b^{2} - 4 a c - 7 = 0$

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 $c$ .

$0^{2} - 4 (1 (- 4 a c - 7))$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$0 - 4 (1 (- 4 a c - 7))$

Multiply $- 4 a c - 7$ by $1$ .

$0 - 4 (- 4 a c - 7)$

Apply the distributive property.

$0 - 4 (- 4 a c) - 4 \cdot - 7$

Multiply $- 4$ by $- 4$ .

$0 + 16 (a c) - 4 \cdot - 7$

Multiply $- 4$ by $- 7$ .

$0 + 16 a c + 28$

Add $0$ and $16 a c$ .

$16 a c + 28$