6=-16t^2+37t+1

Solution for 6=-16t^2+37t+1 equation:

6=-16t^2+37t+1

We move all terms to the left:

6-(-16t^2+37t+1)=0

We get rid of parentheses

16t^2-37t-1+6=0

We add all the numbers together, and all the variables

16t^2-37t+5=0

a = 16; b = -37; c = +5;
Δ = b2-4ac
Δ = -372-4·16·5
Δ = 1049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{1049}}{2*16}=\frac{37-\sqrt{1049}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1049}}{2*16}=\frac{37+\sqrt{1049}}{32}
$