0=-16t^2+263t-214

Solution for 0=-16t^2+263t-214 equation:

0=-16t^2+263t-214

We move all terms to the left:

0-(-16t^2+263t-214)=0

We add all the numbers together, and all the variables

-(-16t^2+263t-214)=0

We get rid of parentheses

16t^2-263t+214=0

a = 16; b = -263; c = +214;
Δ = b2-4ac
Δ = -2632-4·16·214
Δ = 55473
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:

$\sqrt{\Delta}=\sqrt{55473}=\sqrt{1681*33}=\sqrt{1681}*\sqrt{33}=41\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-263)-41\sqrt{33}}{2*16}=\frac{263-41\sqrt{33}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-263)+41\sqrt{33}}{2*16}=\frac{263+41\sqrt{33}}{32}
$