Find the Discriminant 4x^2=-6x-3

$4 x^{2} = - 6 x - 3$

Step 1

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

Add $6 x$ to both sides of the equation.

$4 x^{2} + 6 x = - 3$

Add $3$ to both sides of the equation.

$4 x^{2} + 6 x + 3 = 0$

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 $c$ .

$6^{2} - 4 (4 \cdot 3)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $6$ to the power of $2$ .

$36 - 4 (4 \cdot 3)$

Multiply $- 4 (4 \cdot 3)$ .

Multiply $4$ by $3$ .

$36 - 4 \cdot 12$

Multiply $- 4$ by $12$ .

$36 - 48$

Subtract $48$ from $36$ .

$- 12$