38=-16t^2+80t+6

Solution for 38=-16t^2+80t+6 equation:

38=-16t^2+80t+6

We move all terms to the left:

38-(-16t^2+80t+6)=0

We get rid of parentheses

16t^2-80t-6+38=0

We add all the numbers together, and all the variables

16t^2-80t+32=0

a = 16; b = -80; c = +32;
Δ = b2-4ac
Δ = -802-4·16·32
Δ = 4352
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:

$\sqrt{\Delta}=\sqrt{4352}=\sqrt{256*17}=\sqrt{256}*\sqrt{17}=16\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{17}}{2*16}=\frac{80-16\sqrt{17}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{17}}{2*16}=\frac{80+16\sqrt{17}}{32}
$