0=-16t2+46t+6.

Solution for 0=-16t2+46t+6. equation:

0=-16t^2+46t+6.

We move all terms to the left:

0-(-16t^2+46t+6.)=0

We add all the numbers together, and all the variables

-(-16t^2+46t+6.)=0

We get rid of parentheses

16t^2-46t-6.=0

We add all the numbers together, and all the variables

16t^2-46t-6=0

a = 16; b = -46; c = -6;
Δ = b2-4ac
Δ = -462-4·16·(-6)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-50}{2*16}=\frac{-4}{32}
=-1/8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+50}{2*16}=\frac{96}{32}
=3
$