Find the Discriminant 3x+7=-5x^2-4

$3 x + 7 = - 5 x^{2} - 4$

Step 1

Move all terms to the left side of the equation and simplify.

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

Add $5 x^{2}$ to both sides of the equation.

$3 x + 7 + 5 x^{2} = - 4$

Add $4$ to both sides of the equation.

$3 x + 7 + 5 x^{2} + 4 = 0$

Add $7$ and $4$ .

$3 x + 5 x^{2} + 11 = 0$

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 $c$ .

$3^{2} - 4 (5 \cdot 11)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

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

$9 - 4 (5 \cdot 11)$

Multiply $- 4 (5 \cdot 11)$ .

Multiply $5$ by $11$ .

$9 - 4 \cdot 55$

Multiply $- 4$ by $55$ .

$9 - 220$

Subtract $220$ from $9$ .

$- 211$