0=16t^2+88t+5

Solution for 0=16t^2+88t+5 equation:

0=16t^2+88t+5

We move all terms to the left:

0-(16t^2+88t+5)=0

We add all the numbers together, and all the variables

-(16t^2+88t+5)=0

We get rid of parentheses

-16t^2-88t-5=0

a = -16; b = -88; c = -5;
Δ = b2-4ac
Δ = -882-4·(-16)·(-5)
Δ = 7424
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:

$\sqrt{\Delta}=\sqrt{7424}=\sqrt{256*29}=\sqrt{256}*\sqrt{29}=16\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-16\sqrt{29}}{2*-16}=\frac{88-16\sqrt{29}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+16\sqrt{29}}{2*-16}=\frac{88+16\sqrt{29}}{-32}
$