What is the nature of roots of the quadratic equation

The given quadric equation is $4 x^{2}-12 x-9=0$

Here, $a=4, b=-12$ and, $c=-9$

As we know that $D=b^{2}-4 a c$

Putting the value of $a=4, b=-12$ and, $c=-9$

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

$=144+144$

$=288$

Since, $D \geq 0$

Therefore, root of the given equation are real and distinct.