144t=-16t^2-64

Solution for 144t=-16t^2-64 equation:

144t=-16t^2-64

We move all terms to the left:

144t-(-16t^2-64)=0

We get rid of parentheses

16t^2+144t+64=0

a = 16; b = 144; c = +64;
Δ = b2-4ac
Δ = 1442-4·16·64
Δ = 16640
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:

$\sqrt{\Delta}=\sqrt{16640}=\sqrt{256*65}=\sqrt{256}*\sqrt{65}=16\sqrt{65}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-16\sqrt{65}}{2*16}=\frac{-144-16\sqrt{65}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+16\sqrt{65}}{2*16}=\frac{-144+16\sqrt{65}}{32}
$