0=3+15t-6t^2

Solution for 0=3+15t-6t^2 equation:

0=3+15t-6t^2

We move all terms to the left:

0-(3+15t-6t^2)=0

We add all the numbers together, and all the variables

-(3+15t-6t^2)=0

We get rid of parentheses

6t^2-15t-3=0

a = 6; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·6·(-3)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{33}}{2*6}=\frac{15-3\sqrt{33}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{33}}{2*6}=\frac{15+3\sqrt{33}}{12}
$