23.5=16t^2+8t+5

Solution for 23.5=16t^2+8t+5 equation:

23.5=16t^2+8t+5

We move all terms to the left:

23.5-(16t^2+8t+5)=0

We get rid of parentheses

-16t^2-8t-5+23.5=0

We add all the numbers together, and all the variables

-16t^2-8t+18.5=0

a = -16; b = -8; c = +18.5;
Δ = b2-4ac
Δ = -82-4·(-16)·18.5
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{78}}{2*-16}=\frac{8-4\sqrt{78}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{78}}{2*-16}=\frac{8+4\sqrt{78}}{-32}
$