6=16t^2+38t+2

Solution for 6=16t^2+38t+2 equation:

6=16t^2+38t+2

We move all terms to the left:

6-(16t^2+38t+2)=0

We get rid of parentheses

-16t^2-38t-2+6=0

We add all the numbers together, and all the variables

-16t^2-38t+4=0

a = -16; b = -38; c = +4;
Δ = b2-4ac
Δ = -382-4·(-16)·4
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-10\sqrt{17}}{2*-16}=\frac{38-10\sqrt{17}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+10\sqrt{17}}{2*-16}=\frac{38+10\sqrt{17}}{-32}
$