0=20x^2-12x-9

Solution for 0=20x^2-12x-9 equation:

0=20x^2-12x-9

We move all terms to the left:

0-(20x^2-12x-9)=0

We add all the numbers together, and all the variables

-(20x^2-12x-9)=0

We get rid of parentheses

-20x^2+12x+9=0

a = -20; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-20)·9
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{6}}{2*-20}=\frac{-12-12\sqrt{6}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{6}}{2*-20}=\frac{-12+12\sqrt{6}}{-40}
$