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

Solution for 0=-16t^2+46t-2 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

16t^2-46t+2=0

a = 16; b = -46; c = +2;
Δ = b2-4ac
Δ = -462-4·16·2
Δ = 1988
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:

$\sqrt{\Delta}=\sqrt{1988}=\sqrt{4*497}=\sqrt{4}*\sqrt{497}=2\sqrt{497}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{497}}{2*16}=\frac{46-2\sqrt{497}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{497}}{2*16}=\frac{46+2\sqrt{497}}{32}
$