19=16t^2+36t+5

Solution for 19=16t^2+36t+5 equation:

19=16t^2+36t+5

We move all terms to the left:

19-(16t^2+36t+5)=0

We get rid of parentheses

-16t^2-36t-5+19=0

We add all the numbers together, and all the variables

-16t^2-36t+14=0

a = -16; b = -36; c = +14;
Δ = b2-4ac
Δ = -362-4·(-16)·14
Δ = 2192
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:

$\sqrt{\Delta}=\sqrt{2192}=\sqrt{16*137}=\sqrt{16}*\sqrt{137}=4\sqrt{137}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{137}}{2*-16}=\frac{36-4\sqrt{137}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{137}}{2*-16}=\frac{36+4\sqrt{137}}{-32}
$