Find the Discriminant 4x^2=-12x+9

$4 x^{2} = - 12 x + 9$

Step 1

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

Add $12 x$ to both sides of the equation.

$4 x^{2} + 12 x = 9$

Subtract $9$ from both sides of the equation.

$4 x^{2} + 12 x - 9 = 0$

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 $c$ .

$12^{2} - 4 (4 \cdot - 9)$

Step 4

Evaluate the result to find the discriminant.

Simplify each term.

Raise $12$ to the power of $2$ .

$144 - 4 (4 \cdot - 9)$

Multiply $- 4 (4 \cdot - 9)$ .

Multiply $4$ by $- 9$ .

$144 - 4 \cdot - 36$

Multiply $- 4$ by $- 36$ .

$144 + 144$

Add $144$ and $144$ .

$288$