27.5=16t^2+2t

Solution for 27.5=16t^2+2t equation:

27.5=16t^2+2t

We move all terms to the left:

27.5-(16t^2+2t)=0

We get rid of parentheses

-16t^2-2t+27.5=0

a = -16; b = -2; c = +27.5;
Δ = b2-4ac
Δ = -22-4·(-16)·27.5
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-42}{2*-16}=\frac{-40}{-32}
=1+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+42}{2*-16}=\frac{44}{-32}
=-1+3/8
$