0=9t^2-6t-12

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

0=9t^2-6t-12

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -9; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-9)·12
Δ = 468
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{13}}{2*-9}=\frac{-6-6\sqrt{13}}{-18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{13}}{2*-9}=\frac{-6+6\sqrt{13}}{-18}
$