0=-6t^2+12t+60

Solution for 0=-6t^2+12t+60 equation:

0=-6t^2+12t+60

We move all terms to the left:

0-(-6t^2+12t+60)=0

We add all the numbers together, and all the variables

-(-6t^2+12t+60)=0

We get rid of parentheses

6t^2-12t-60=0

a = 6; b = -12; c = -60;
Δ = b2-4ac
Δ = -122-4·6·(-60)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{11}}{2*6}=\frac{12-12\sqrt{11}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{11}}{2*6}=\frac{12+12\sqrt{11}}{12}
$