100=144t-16t2

Solution for 100=144t-16t2 equation:

100=144t-16t^2

We move all terms to the left:

100-(144t-16t^2)=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 = 14336
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:

$\sqrt{\Delta}=\sqrt{14336}=\sqrt{1024*14}=\sqrt{1024}*\sqrt{14}=32\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-32\sqrt{14}}{2*16}=\frac{144-32\sqrt{14}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+32\sqrt{14}}{2*16}=\frac{144+32\sqrt{14}}{32}
$