0=16t^2+30t+1

Solution for 0=16t^2+30t+1 equation:

0=16t^2+30t+1

We move all terms to the left:

0-(16t^2+30t+1)=0

We add all the numbers together, and all the variables

-(16t^2+30t+1)=0

We get rid of parentheses

-16t^2-30t-1=0

a = -16; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·(-16)·(-1)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{209}}{2*-16}=\frac{30-2\sqrt{209}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{209}}{2*-16}=\frac{30+2\sqrt{209}}{-32}
$