Find the Discriminant 14r^2=5-7r

$14 r^{2} = 5 - 7 r$

Step 1

Move all the expressions to the left side of the equation.

Subtract $5$ from both sides of the equation.

$14 r^{2} - 5 = - 7 r$

Add $7 r$ to both sides of the equation.

$14 r^{2} - 5 + 7 r = 0$

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 $c$ .

$7^{2} - 4 (14 \cdot - 5)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $7$ to the power of $2$ .

$49 - 4 (14 \cdot - 5)$

Multiply $- 4 (14 \cdot - 5)$ .

Multiply $14$ by $- 5$ .

$49 - 4 \cdot - 70$

Multiply $- 4$ by $- 70$ .

$49 + 280$

Add $49$ and $280$ .

$329$