0=9t^2-12t-12

Solution for 0=9t^2-12t-12 equation:

0=9t^2-12t-12

We move all terms to the left:

0-(9t^2-12t-12)=0

We add all the numbers together, and all the variables

-(9t^2-12t-12)=0

We get rid of parentheses

-9t^2+12t+12=0

a = -9; b = 12; c = +12;
Δ = b2-4ac
Δ = 122-4·(-9)·12
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*-9}=\frac{-36}{-18}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*-9}=\frac{12}{-18}
=-2/3
$