10=-6t^2+30t+1

Solution for 10=-6t^2+30t+1 equation:

10=-6t^2+30t+1

We move all terms to the left:

10-(-6t^2+30t+1)=0

We get rid of parentheses

6t^2-30t-1+10=0

We add all the numbers together, and all the variables

6t^2-30t+9=0

a = 6; b = -30; c = +9;
Δ = b2-4ac
Δ = -302-4·6·9
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{19}}{2*6}=\frac{30-6\sqrt{19}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{19}}{2*6}=\frac{30+6\sqrt{19}}{12}
$