0=3t^2-9t-7

Solution for 0=3t^2-9t-7 equation:

0=3t^2-9t-7

We move all terms to the left:

0-(3t^2-9t-7)=0

We add all the numbers together, and all the variables

-(3t^2-9t-7)=0

We get rid of parentheses

-3t^2+9t+7=0

a = -3; b = 9; c = +7;
Δ = b2-4ac
Δ = 92-4·(-3)·7
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{165}}{2*-3}=\frac{-9-\sqrt{165}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{165}}{2*-3}=\frac{-9+\sqrt{165}}{-6}
$