0=-16t^2+46t+12

Solution for 0=-16t^2+46t+12 equation:

0=-16t^2+46t+12

We move all terms to the left:

0-(-16t^2+46t+12)=0

We add all the numbers together, and all the variables

-(-16t^2+46t+12)=0

We get rid of parentheses

16t^2-46t-12=0

a = 16; b = -46; c = -12;
Δ = b2-4ac
Δ = -462-4·16·(-12)
Δ = 2884
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:

$\sqrt{\Delta}=\sqrt{2884}=\sqrt{4*721}=\sqrt{4}*\sqrt{721}=2\sqrt{721}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{721}}{2*16}=\frac{46-2\sqrt{721}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{721}}{2*16}=\frac{46+2\sqrt{721}}{32}
$