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

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

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

Subtract $12 x$ from both sides of the equation.

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

Add $9$ to both sides of the equation.

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

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Substitute in the values of $a$ , $b$ , and $c$ .

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

Evaluate the result to find the discriminant.

Simplify each term.

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

$144 - 4 (4 \cdot 9)$

Multiply $4$ by $9$ .

$144 - 4 \cdot 36$

Multiply $- 4$ by $36$ .

$144 - 144$

Subtract $144$ from $144$ .

$0$