0=-16t^2+144t+100

Solution for 0=-16t^2+144t+100 equation:

0=-16t^2+144t+100

We move all terms to the left:

0-(-16t^2+144t+100)=0

We add all the numbers together, and all the variables

-(-16t^2+144t+100)=0

We get rid of parentheses

16t^2-144t-100=0

a = 16; b = -144; c = -100;
Δ = b2-4ac
Δ = -1442-4·16·(-100)
Δ = 27136
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:

$\sqrt{\Delta}=\sqrt{27136}=\sqrt{256*106}=\sqrt{256}*\sqrt{106}=16\sqrt{106}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-16\sqrt{106}}{2*16}=\frac{144-16\sqrt{106}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+16\sqrt{106}}{2*16}=\frac{144+16\sqrt{106}}{32}
$