100=16t^2+92t+24

Solution for 100=16t^2+92t+24 equation:

100=16t^2+92t+24

We move all terms to the left:

100-(16t^2+92t+24)=0

We get rid of parentheses

-16t^2-92t-24+100=0

We add all the numbers together, and all the variables

-16t^2-92t+76=0

a = -16; b = -92; c = +76;
Δ = b2-4ac
Δ = -922-4·(-16)·76
Δ = 13328
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:

$\sqrt{\Delta}=\sqrt{13328}=\sqrt{784*17}=\sqrt{784}*\sqrt{17}=28\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-28\sqrt{17}}{2*-16}=\frac{92-28\sqrt{17}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+28\sqrt{17}}{2*-16}=\frac{92+28\sqrt{17}}{-32}
$