0=4x^2-12x-9

Solution for 0=4x^2-12x-9 equation:

0=4x^2-12x-9

We move all terms to the left:

0-(4x^2-12x-9)=0

We add all the numbers together, and all the variables

-(4x^2-12x-9)=0

We get rid of parentheses

-4x^2+12x+9=0

a = -4; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-4)·9
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*-4}=\frac{-12-12\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*-4}=\frac{-12+12\sqrt{2}}{-8}
$