0=-16t^2+47t+1

Solution for 0=-16t^2+47t+1 equation:

0=-16t^2+47t+1

We move all terms to the left:

0-(-16t^2+47t+1)=0

We add all the numbers together, and all the variables

-(-16t^2+47t+1)=0

We get rid of parentheses

16t^2-47t-1=0

a = 16; b = -47; c = -1;
Δ = b2-4ac
Δ = -472-4·16·(-1)
Δ = 2273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{2273}}{2*16}=\frac{47-\sqrt{2273}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2273}}{2*16}=\frac{47+\sqrt{2273}}{32}
$