0=16t^2-88t+100

Solution for 0=16t^2-88t+100 equation:

0=16t^2-88t+100

We move all terms to the left:

0-(16t^2-88t+100)=0

We add all the numbers together, and all the variables

-(16t^2-88t+100)=0

We get rid of parentheses

-16t^2+88t-100=0

a = -16; b = 88; c = -100;
Δ = b2-4ac
Δ = 882-4·(-16)·(-100)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-8\sqrt{21}}{2*-16}=\frac{-88-8\sqrt{21}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+8\sqrt{21}}{2*-16}=\frac{-88+8\sqrt{21}}{-32}
$