0=3t2+6t-9

Solution for 0=3t2+6t-9 equation:

0=3t^2+6t-9

We move all terms to the left:

0-(3t^2+6t-9)=0

We add all the numbers together, and all the variables

-(3t^2+6t-9)=0

We get rid of parentheses

-3t^2-6t+9=0

a = -3; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-3)·9
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*-3}=\frac{-6}{-6}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*-3}=\frac{18}{-6}
=-3
$