0=6x^2-12x-9

Solution for 0=6x^2-12x-9 equation:

0=6x^2-12x-9

We move all terms to the left:

0-(6x^2-12x-9)=0

We add all the numbers together, and all the variables

-(6x^2-12x-9)=0

We get rid of parentheses

-6x^2+12x+9=0

a = -6; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-6)·9
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{10}}{2*-6}=\frac{-12-6\sqrt{10}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{10}}{2*-6}=\frac{-12+6\sqrt{10}}{-12}
$