0=-16t^2+43t+3

Solution for 0=-16t^2+43t+3 equation:

0=-16t^2+43t+3

We move all terms to the left:

0-(-16t^2+43t+3)=0

We add all the numbers together, and all the variables

-(-16t^2+43t+3)=0

We get rid of parentheses

16t^2-43t-3=0

a = 16; b = -43; c = -3;
Δ = b2-4ac
Δ = -432-4·16·(-3)
Δ = 2041
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{-(-43)-\sqrt{2041}}{2*16}=\frac{43-\sqrt{2041}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{2041}}{2*16}=\frac{43+\sqrt{2041}}{32}
$