100=-4t^2+64t+144

Solution for 100=-4t^2+64t+144 equation:

100=-4t^2+64t+144

We move all terms to the left:

100-(-4t^2+64t+144)=0

We get rid of parentheses

4t^2-64t-144+100=0

We add all the numbers together, and all the variables

4t^2-64t-44=0

a = 4; b = -64; c = -44;
Δ = b2-4ac
Δ = -642-4·4·(-44)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-40\sqrt{3}}{2*4}=\frac{64-40\sqrt{3}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+40\sqrt{3}}{2*4}=\frac{64+40\sqrt{3}}{8}
$