0=3t^2-6t-10

Solution for 0=3t^2-6t-10 equation:

0=3t^2-6t-10

We move all terms to the left:

0-(3t^2-6t-10)=0

We add all the numbers together, and all the variables

-(3t^2-6t-10)=0

We get rid of parentheses

-3t^2+6t+10=0

a = -3; b = 6; c = +10;
Δ = b2-4ac
Δ = 62-4·(-3)·10
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{39}}{2*-3}=\frac{-6-2\sqrt{39}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{39}}{2*-3}=\frac{-6+2\sqrt{39}}{-6}
$